We just released the first bits of character progression. You can get to it by hitting "profile" on the main screen, then "View Upgrades".
You can upgrade four stats (there are two more coming in the future), which will make your character progressively more powerful when fighting single player opponents. Right now, Upgrades aren't applied in multiplayer, because it'd make the game more about who was higher level, not who played the best. And with relatively few players, we can't effectively "match" players with opponents of similar level. We do hope to be able to do that at some point when there are more people playing, we just can't do it yet.
We've also introduced more interesting enemies in Single Player. First, the AI has had a huge upgrade over a week ago. It'll play *much* smarter. Should be significantly more of a challenge. Also, as you get higher level, your enemies will start to have "perks" that make them more powerful. Click on the enemy profile, and you'll be able to see what perks they have active. More perks = more rewards, so it's a good thing.
But this isn't even close to where we want single player to end up. One of the biggest changes is going to be that you'll start the day with a certain amount of health, and that will carry over between fights. But you won't be fighting just characters with as much health/shield as you - there will be a wider variety of enemies (though at the start they'll all look basically the same). So the character progression + enemies & enemy progression will be part of a larger structure that'll ALSO do some fairly weird stuff you haven't seen before.
If you get a chance to give the new Upgrades & Single Player a shot, let us know what you think! And keep an eye out for what's coming next. You won't have long to wait.