Okay, so, Gloomhaven.
First, you make your party. There are six classes available to start with, including the Brute, Tinkerer, Spellweaver, Scoundrel, Cragheart and Mindthief. Each player (up to 4 total) picks one of the available classes, opens up the class tuckbox, and pours out the contents. You get a notepad of character sheets for that class, a standee, a few class tokens, a big ol' set of class cards (you will only have the level 1 and X cards available to start), some class-specific cards you'll eventually be able to add to your character's combat modifier deck, and a class mat with art, HP and XP trackers, and your hand size for that class. You'll name your character, mark down a starting cash pool of 30 gold, and draw two Personal Story cards (pick one, discard the other), which give you this character's goal in being an adventurer. Achieve that goal, and your character will retire, unlocking various things in the process. (At which point you create a new character). You also name your party, and it starts at a reputation of 0. As you adventure, you keep track of your party's reputation, unlocked party achievements (mostly gating scenarios), location (which scenario you're going back to, mostly), etc. My friends picked the Tinkerer and Brute. I went with the Mindthief.
Once you've got your party assembled, you open up the scenario book and kick off by adding the first scenario location (the Black Barrow) to the world map and placing a Global Achievement sticker to note that Gloomhaven's government is "Militaristic" (no idea what this does yet), and then you can poke around the city for a moment to prep by buying gear, optionally have a city event (we found some mislaid supplies that we could have either sold, or turned over to the guard - we did the latter), and hit the road to the Barrow. Which means you draw a road event (in this case, we fell into an underground structure and decided to explore it, to an uncertain payoff). And then you set up the scenario, like you would in things like Descent, by assembling map tiles and populating the visible part with enemies, treasure and so forth, and you give everyone two secret battle goals, pick one. If you win the scenario and completed your goal, you get the listed check(s) on your character sheet. Get three and get a perk (which changes your modifier deck).
Once you're actually in the scenario, the structure is fairly straightforward. You have class cards available equal to your hand size, and each turn you select two (face down) and pick one as your "leading" card, or you decide to take a "long rest" (more on this in a second). Once everyone has done this, you flip up your leading cards and deal a monster action card for each type of monster currently on the map. You compare the initiative order on everyone's leading cards to the monster action cards and that determines turn order. Then everyone flips up the other card as well, and you act in turn order. Characters use the top half of one card and the bottom half of the other, in either order (and which card you used for initiative is irrelevant at this stage), and do each step of that half from top to bottom. You can skip any portion of the card except for things that harm you or an ally if you so choose, and can optionally use any top half as an Attack 2, or any bottom half as a Move 2. You can also potentially use any items you have with you according to the text on their card. Monsters act by type, starting with any elite members of that type and continuing with normal monsters of that type, in the order of their figure number. They will take whatever actions are on their card, top to bottom, if able, and focus on the closest (by number of moves required to maximize their attack) enemy, preferring the faster one if there is a tie.
Attacks are made with the printed value on the attack card, or the printed attack value of the monster, depending. Then any intrinsic offensive modifiers (most commonly on monster actions) are applied. Then the attacker draws a modifier card from their modifier deck for each target (each character has one, and the monsters share one) and applies that (ranging by default from one -2 through one +2 1x with plenty of +0 and -1 in between, as well as one 2x Damage and one No Damage that reshuffle the deck at the end of the round if hit). And finally any defensive modifiers (Shield, for example) are applied, and damage is resolved. Damage to characters is tracked on their mat, damage to monsters is tracked on these ingenious sleeves that fit over the monster cards to limit the display to the stats for the current monster level (between 0 and 7) and have spaces for 6 or 10 numbered monsters of that type. Unlike some games of this sort, additional status effects (like poison or stun) are applied even if the attack didn't do damage. If a PC is reduced to 0 health, they're out of the scenario but will recover without ill effect afterwards, win or lose. If a monster is reduced to 0 they are removed from the map and, if they were placed by the scenario (as opposed to being summoned) they drop a money token.
Once everyone has gone around and done their stuff, the class cards you used go into either the discard pile or sometimes the lost pile depending (some powerful actions automatically are lost after they're used), any modifier and monster action decks that have hit a card with a reshuffle symbol are reshuffled, and you loot any money or treasure chest you are standing on.
So here's the big wrinkle: in order to get your cards back from the discard pile (without some sort of special effect, be it action or item), you have to rest. This can either be a short rest (which happens at the end of the round), or a long rest (which takes your whole turn). Also, you -must- play two cards on your turn, so if you don't have enough to do this, you are forced to take a long rest. A short rest obviously gets you up and running faster, but if you do that, once you've refilled your hand from your discards, you have to turf a random card into your lost pile. And you don't recover those at all during the scenario, barring special effects. A long rest, on the other hand, still requires you to put a card in that lost pile...but you get to pick which one. Furthermore, it heals you by 2 HP and refreshes any spent items (consumed items, like potions, are gone until the end of the scenario). The downside, of course, is missing out on a turn. Finally, if you have only one, or zero cards left in your hand -and- discard, then you're out of the scenario, because you can no longer play two cards or rest, either one.
Oh, and you can cancel an instance of damage by putting a card from your hand or two cards from your discard into your lost pile. Better than getting knocked out straight away, right?
This ends up being incredibly tactical and varied and interesting. Every class has hugely distinct card designs - the Tinkerer was doing party buffs, healing, and had a lot of one shot ranged gadgets. The Brute was charging around and trampling things and doing big sweeping area attacks or enormous single attacks. My Mindthief was summoning hordes (well, a horde) of rats, mind controlling enemies into attacking one another or walking into traps (knocking enemies into traps was a GREAT way to clear the traps and kill enemies in one fell swoop), dashing up for rapid fire poisoned dagger strikes or sniping with stunning cold, and could psychically augment his attacks (I mainly used the health leech, but damage or shielding were also options). We had a really rotten first turn (the Bandit Guards, all six of them, got their best action card and beat us on initiative so they swarmed us and poisoned all three of us with hard-hitting attacks, then had damage reduction in place for our subsequent retaliation - I had to lose two cards straight off the bat to stay alive), and at one point the archers in the second room immobilized me three freaking turns in a row, but we did eventually finish the scenario -and- loot the treasure (permanent unlocks ahoy). I for one was pretty much sucking fumes by the end because of that early card loss, but that was fine because my battle goal was to have 3 or fewer cards in hand or discard by scenario end, so I definitely got my check.
After that, we unlocked scenario 2 on the map, got a party achievement (First Steps), tallied up our earned gold and XP (I came out ahead on XP because I'd used so many XP-granting cards during the scenario, but everyone gets some for the scenario win), got our unlock for the treasure (I won't say what), and decided to continue to scenario 2 next time rather than doing road events to and from Gloomhaven to...well, not accomplish much because we didn't exactly have a ton of gold on hand, weren't going to level, and didn't need to make new characters etc.
I apologize for the length of the post but there's a lot going on in Gloomhaven and it's all awesome.