In general, Elysium is a set collection game, with players drafting fifteen cards over the course of five rounds, then trying to assemble those cards into legends (sets of cards organized by rank or family) before the game ends. More flavorfully, players compete to claim and use characters and objects from Greek mythology into legends, with these characters and objects being grouped into eight families: Zeus, Hermes, Apollo, Ares, Athena, Hades, Hephaestus and Poseidon.
In slightly more detail, each round starts with players having columns in four colors, and they're presented with cards and order tiles, with each of these items having a cost in one or two colors. Players take turns drafting three cards and one order tile, in whatever order they like, but to claim something they need to have the required column colors in front of them. After each item they claim, they must set aside any one color out of play, thereby reducing their options on future turns.
What provides the juice in the game, aside from the competition, is the special powers on the cards: cards affiliated with Zeus grant you ways to score points during the game; those with Hades help you bring more cards into the afterlife, the Elysian Fields where legends are worth VPs at game's end; Hephaestus helps you earn money, which you need to bring cards to the afterlife; Poseidon attacks the opponents' holdings; and so on. Some cards provide an immediate benefit, some a one-shot power, some a power you can use every turn, and so on — but you can use these powers only so long as the cards are still in your active area and haven't been transferred to the afterlife (although Hermes' cards sometimes let you evade this restriction).
You're making and breaking card combinations over the course of the game, and with only five of the eight families in play each game, the nature of the gameplay differs depending on which cards are in the mix:
• Without Hades, transferring cards to the afterlife is much more dependent on the order tile (which determines turn order for the next round, in addition to giving you some amount of money, VPs, and allowable transfers)
• Without Athena, you can't rely on abilities shared by opponents
• Without Hephaestus, you'll have a harder time collecting money
• With Ares, you'll also be fighting for a majority of prestige points, in addition to everything else you're doing
• With Apollo, you can see some of the cards coming in the subsequent round and possibly even use those cards during the current round
Everything changes depending on which families are in play as well as what comes out each round. Since you put out 3N+1 cards each round (with N = number of players), with fewer players you see fewer cards, and thus you have to learn to make do with what's available to you. For this and a few other reasons, Elysium reminds me of a streamlined Seasons. You develop a plan based on what's initially available to you, then you keep modifying that plan based on what comes available each round. Sometimes a player gets lucky by being the first player in a round and having first crack at something super beneficial to whatever their plan is, but that's life. If you think that's a real issue in Elysium, then you can go out of your way to claim the first player tile each round, but that's probably not a great idea since you're then ceding first shot at the cards to everyone else. As in most games, you can't have everything, so you make do the best you can.
Why Elysium feels more streamlined than Seasons is that players don't have to muck about with resources, worrying about getting that one fire token so that you can cast this spell, which you definitely want to cast before this other spell, which you want to make sure is in play before the end of the year, and so on. No, you have only the four columns available to you, and as players spend their columns, you track who can acquire which things and make guesses as to what they might want to acquire, balancing all of this against what might be best for you.
What's more, since you must transfer cards to your Elysian Fields over the course of the game — well, you don't have to, but you can't transfer everything in the final round, so if you want a shot at winning, you had best transfer things there bit by bit in order to compile decent legends by game's end — you're not overwhelmed by choices from the cards in front of you. You see something fruitful, squeeze it for a few turns to bathe in its rich juices, then move it on to make room for something else. (This description might also apply to those of us who play games a few times, then move on to something else. It's a coincidence, I swear!)
This whittling away at your holdings might be why most of my Elysium games have finished in under an hour while games of Seasons typically stretch to two hours. This difference could be part of why Elysium got the nod for Kennerspiel, with the design packing lots of decisions in a tighter timeframe. The gorgeous art on the cover and cards is a nice plus, too.