The mission timer doesn't start until the squad breaks Concealment. Can only occur on missions that have a timer.
Only soldiers of Sergeant or below may be deployed on the mission. The mission always has the sub-Sitrep of Low Alert, reducing how many enemies are on the map.
The mission is dotted with crates that can be opened to acquire randomized loot. You do
automatically acquire the loot from untouched crates if you win the mission, even if it's a mission X-COM sticks around and loots everything in.
Squad size limited to 3. Timer extended by 2 turns. Somehow incompatible with Chosen and Alien Rulers.
...oh, and it turns out Surgical is bugged. It's supposed to switch pods from being 3-enemy groups to being 2-enemy groups, but is... unreliable about actually doing so. To the point I personally have never seen this behavior successfully fire. There's a mod to fix this, at least.
High Explosives
The mission is dotted with explosive terrain objects that can be targeted by units to detonate them.
This is usually primarily an advantage. The AI will never deliberately target environmental explosives, and plenty of enemies can't trigger them accidentally. You should still avoid taking Cover nearby these explosives in case an ADVENT Trooper remembers they're carrying a grenade, but the point is you can generally treat this as a helpful Covert Op.
Qualifier: you're trying to not wreck the environment in Supply Raids, and it's easy to end up destroying supply crates by catching an explosive with an area-of-effect attack, or to opportunistically detonate an explosive and then to your dismay the fire it starts destroys supply crates. Or even to take a shot, miss, have it start a fire, and then the fire detonates an explosive you were trying to not blow up!
Still, in Guerrilla Ops it's usually a positive, or at least not a negative.
This is an idea that would be more interesting if XCOM 2 was using physics on projectiles like classic X-COM, forcing you to think twice about a given shot. In actual XCOM 2, it really is mostly just... more opportunities to blow up enemies, plus occasional frustration in Supply Raid missions. It's not terrible or anything, but it's a poor fit to the game.
Show of Force
Makes everything all ADVENT, no Aliens.
This also somewhat inconsistently increases maximum pod size to 4 enemies per pod. As in, I've had times where every pod on the map was made of 4 enemies, and other times where no pod went above 3. I'm not entirely sure what causes this.
Regardless, note that as usual Mecs and Turrets are counted as ADVENT units and so can show up in a Show of Force mission.
This would be more interesting if Aliens were more distinct from ADVENT forces, not to mention if ADVENT-majority wasn't already the default. War of the Chosen is more prone to Alien-dominant forces, and from earlier in the game, but it still defaults pretty strongly to maps being ADVENT-heavy. So this is kind of a neat idea in principle, but doesn't feel very distinctive in practice.
Alas.
The Lost
The mission has Lost present. Also adds 2 turns to the mission timer, if the mission has a timer.
This is one of the most dramatic Sitreps, and probably basically the entire reason the Sitreps system even exists. An entire third faction in turn order, one that is a radically different experience to fight, and which due to Lost wave mechanics has much deeper implications than just the part where you're fighting a non-standard enemy type that normally can't show up in any ol' mission? That's multiple layers of huge.
A particularly interesting mechanics interaction is that if The Lost triggers on a mission where you're defending a destructible object, the AI's willingness to take potshots in the fog will extend to shooting at the Lost. The Lost won't activate in response to being shot (Unless your squad has sight on them), and each pod will only be willing to have their pod leader take a shot, with this being limited to once per pod per turn, so Headshot mechanics are irrelevant to it. This has the side effect of giving you advance warning on the general location of ADVENT/Alien pods, and also means that in those missions in particular the Lost will tend to be slightly less of a problem, taking injuries and losses before you even encounter them.
In War of the Chosen your very first Resistance-provided mission will always, if you don't have Lost And Abandoned turned on, have either The Lost or The Horde attached to it. This particular example is the game being artificial, but as I've alluded to already it's also the case that some mission sub-types are premised under Lost presence and so will always present as having The Lost Sitrep. (Though it's not a properly rolled Sitrep and can be stacked atop a properly rolled other Sitrep) Less consistent and less obvious is that some missions can have Lost presence, but it's not guaranteed and depends on the map type; Supply Extraction missions are one example, where they can either pick a map type of an ADVENT supply depot in the woods, in which case there's no Lost unless the Sitrep roll per se picks The Lost, or it can pick an 'Old World' city map type, in which case Lost will be guaranteed. Which incidentally means you can mostly-reliably predict map type in Supply Extraction missions; if they don't have The Lost, they must be the ADVENT supply depot map type, while if they do generate with The Lost it's extremely likely that they're an Old World city map. This is genuinely somewhat useful to know ahead of time; Old World maps are 100% consistent about having high ground for Skirmishers to make use of, and also 100% consistent about being the kind of map Reapers are particularly important to bring if you want to avoid stumbling into a pod unawares, whereas the ADVENT supply depot map is fairly flat and a Reaper is still helpful but not particularly essential. That kind of thing.
I'll be talking about this more when we get to the Lost themselves, but Lost presence broadly discourages using explosives, encourages bringing Sharpshooters (Templar can also work, though I consider it a bit of a waste of their abilities), makes the Flamethrower maybe worth actually bringing, and makes Expanded Magazines and Automated Reloaders more of a priority than usual. It also makes it harder to set up an Overwatch ambush, because Lost can activate ADVENT pods, and Overwatch ambushes only function on inactive pods.
This is also the main Sitrep that has me skeptical the Alert Level system really properly works, as the files are pretty clear that there's supposed to be fewer ADVENT/Alien pods on the map with the Lost making up the difference, but my experience is that The Lost has no effect on such counts; the Lost are just thrown in atop the ADVENT/Alien forces. This is extremely blatant early in the game, when missions are at their most rigid and predictable, but never stops being true.
The Horde
The mission is made entirely of Lost, though the Chosen can spawn in regardless. If the mission type would normally generate ADVENT reinforcements, The Horde disables that behavior. Also adds 2 turns to the mission timer, if the mission has a timer.
Interestingly, The Horde can only occur on a limited sub-set of missions. Straight from the config files:
ValidMissionTypes="Recover"
ValidMissionTypes="Recover_ADV"
ValidMissionTypes="Recover_Vehicle"
ValidMissionTypes="Recover_Train"
ValidMissionTypes="Hack"
ValidMissionTypes="Hack_ADV"
ValidMissionTypes="Hack_Train"
ValidMissionTypes="DestroyRelay"
ValidMissionTypes="Extract"
ValidMissionTypes="Rescue_AdventCell"
ValidMissionTypes="Rescue_Vehicle"
ValidMissionTypes="SabotageTransmitter"
So basically only missions in which ADVENT is supposed to be escorting or defending something important, and the Horde implicitly changes the narrative to them having given up in the face of the Lost.
Note that the Horde will generally result in an absolutely massive number of Lost in a basically contiguous mass between you and the objective. They'll technically be discrete pods, but with so many of them packed so close together it's fairly difficult to tell where one starts and another begins, and due to Lost sound mechanics once you've started shooting you'll end up pulling even more Lost immediately.
Also note that it will, appropriately enough, prevent civilians from spawning in. Among other points, this means it will actually overrule Alien Infiltrator, preventing any Faceless from spawning in because they have no civilians to hide among. I'm similarly pretty sure that it will prevent Alien Rulers from spawning in, though it's possible I've just never had the stars align the right way for it to happen.
It's worth pointing out that in The Horde missions squad Concealment is pretty worthless, and there's not a ton of reason to concern yourself with preserving it, particularly if you have a Reaper to perform advance scouting. An Overwatch ambush is worse than useless, since Lost not only don't take Cover but the Headshot mechanic means that regular shots can clear out a lot more Lost than Overwatch shots can, and Lost Dashers are the only sub-type that moves fast enough to potentially attack your soldiers the same turn you activated them unless you either moved someone incredibly recklessly or had Lost outright hidden inside a building or something such that you didn't activate them until they were right on top of you...
... and Lost Dashers are never generated in an inactive state at the start of a mission, so it's always safe to move forward and activate new Lost pods so long as you're not moving extremely aggressively.
The only reason to consider not just picking a fight with Lost the instant you can see them in a The Horde mission is that the Chosen can still spawn in, and still wait until squad Concealment is broken before doing so. And that's really more a reason to consider having a Silent Killer Reaper clear out Lost, not a reason to delay fighting Lost at all. And personally I find that so tedious -you have to sit through the Reaper's Shadow break check every single time- that I don't bother. It's not necessary, not even on Legend.
Overall, while The Horde is a neat idea on several levels (I really like the flavor of 'ADVENT just plain gave up and left in the face of infinite zombies'), I'm happy with the fact that it's pretty rare to encounter it. As an occasional change of pace it's fine, but fighting just Lost is a fairly flat gameplay experience, and would get very dull very quickly if it was something you had to do a lot more regularly.
Psionic Storm
The enemy composition will be nearly exclusively psionically capable enemies, meaning Sectoids, ADVENT Priests, Codices, Spectres, and Gatekeepers.
Psionic Storm rolling early in the game is very constrictive on enemy lists, since only Sectoids and basic ADVENT Priests are in the spawn tables from the start of the game, out of psionic enemies. There will usually be a lone ADVENT Trooper or some such on the map, but mostly it'll just be pods of Sectoids and Priests. This can be surprisingly dangerous, as while Sectoids and ADVENT Priests normally prefer to focus on using their special abilities, when multiple of them are active it's much more likely for one to use an ability and then the following ones take shots or at least enter Overwatch. So if you're expecting them to give you a turn of relative safety... nah.
Mind, the alternative would be risking your entire squad getting Mind Controlled in one turn, so this is probably less terrifying in practice. And regardless, very early on it means that instead of half the enemies being 3-4 HP basic ADVENT Troopers, you're dealing with nothing but enemies who have 7+ HP.
It can also be quite nasty if you get it shortly after Skulljacking an ADVENT Officer, as it can result in large numbers of Codices, when Codices are really designed to be something of an early-game boss fight when there's one Codex, and indeed are tuned to still be an above-average enemy in the endgame. Facing multiple pods of them when you haven't even transitioned to magnetic weapons at all? Yikes.
As Templar have some abilities that perform better when facing psionic opponents, you should give more consideration to bringing a Templar along into a Psionic Storm mission. Especially since Sectoids are susceptible to melee. (Which incidentally encourages Ranger use) Similarly, Stocks are worth considering to reliably deal with Sustaining Priests, Mind Shields are worth considering in general since Sectoids and Priests will waste their turns on psionic actions against Mind Shielded soldiers, or Psi Operatives with Solace if you're late enough to have that, and past the very early game... uh, Bluescreen Rounds and EMP Grenade, actually. Three of the five enemies that Psionic Storm focuses on are digital enemies susceptible to these Items!
That's honestly one of the more interesting elements of XCOM 2 to me, that instead of 'psychic enemy' and 'digital enemy' being mutually exclusive they have fairly heavy overlap. It's unusual, and is one of the reasons I'm clear XCOM 2 has a radically different conception of psychic powers than the prior game, as well as why I'm interested in seeing what XCOM 3 does with psionics.
Automated Defenses
The enemy composition will be nearly exclusively robotic enemies, specifically ADVENT Mecs, Spectres, ADVENT Turrets, Codices, and Sectopods.
ADVENT Mecs and Turrets are the only enemies that are in the table in the early game, which can make an early Automated Defenses astonishingly dangerous; the result will be that every pod is 2-3 Mecs at a phase of the game where they're intended to be restricted to being pod leaders supported by less durable units like ADVENT Troopers. This is, in fact, one of the most dangerous Sitreps to roll toward the beginning of the game; blobs of 8 HP, 2 Armor enemies before you even have Shredder on anyone and your best damage is 4-6 is kind of terrifying.
Once you've gotten Codices into the spawn table, and especially once Spectres enter rotation, it becomes much less worrisome, as these operate on the 'will be very dangerous if you give them more than one turn' model of enemy design, instead of Mecs operating under the 'will do damage right now' model. Spectres are also in the general vicinity of when it's reasonable to acquire Bluescreen Rounds, which of course makes Automated Defenses much easier to fight through, since literally everything it focuses on is susceptible to them. (And EMP Grenades, for that matter)
Savage
The enemy composition will be nearly entirely 'monstrous' Aliens, meaning Chryssalids, Faceless, and Muton Berserkers. Note that Faceless forced by this Sitrep will
not start out disguised as a civilian.
If you roll this early in the game, you'll end up with the unusual enemy composition of basically pure Faceless. (They can potentially lead Stun Lancers, but 'nothing but Faceless' is pretty normal) It's also not unusual for Savage to actually be your first encounter with Chryssalids, as they can end up entering rotation notably before a Retaliation mission is actually scheduled. Berserkers showing up is the primary way you'll get non-Savage enemies in a Savage encounter, as they can be leaders to stuff like Mutons and Stun Lancers, and the game will normally refuse to have a Berserker-only pod, and they can't lead Faceless, so the pods will end up rounded out by Stun Lancers or whatever.
Also, like with the Lost Sitrep, this can produce strange results in Defend The Device missions, as the Berserker ability to decide to target allies can lead to Berserkers killing their podmates while the pod is inactive. It's not even restricted to only one Berserker doing so per turn or anything. As such, this can be, bizarrely enough, a boon on Protect The Device missions.