They also know when you're completely surrounded and they all decide to declare war on you. Fortunately there's no happiness levels in your cities, so being stuck in a long war doesn't have a negative side effect, so you can keep cranking out the defensive units and researching without slowing down. In fact, all of the little things that slow you down during the game (unhappiness, revolts, pollution, healthiness, etc) are gone, and it definately helps the game go faster. You don't have to micromanage quite as much.
I've gotten a few games in now. It keeps track of your victories per leader, per level. For example, when starting a new game on "King", when I scroll through the leaders, there are 4 icons at the top of the screen, which show me that I've gotten a diplomatic victory with Alexander and a Domination victory with Shaka. It's a nice pseudo-achievement tracker.
The thing that seems to shock me the most, is that there are so few buildings and units. You'll research a technology and it will only give you access to a world wonder and the next tech on the tree. No other buildings or units. It's nice because if you gain a city later in the game, you don't have to catch up on a lot of building to get it really going. And because there aren't a lot of units, you don't waste as much time building some, only find them obsolete at the next tech.
In the PC games, I don't usually put a lot of effort into a naval force/exploration early in the game, but they really reward you here. If you have a strong naval army, park them next to the coastal city you want to attack, and you'll get a bombardment bonus. They strike first, damaging the enemy at half their strength. And if you don't have a fleet? Then you're on the receiving end, and it's not going to go well.
I really like the hidden "artifacts" on the map. Once you claim them, you get a bonus of some sort. Usually an advanced tech, but I've also gotten gold, a spy, and units. In one game, the Knights Templar gave me a tank. In the 1700s. (Or was it 1500s? I forget now.) And it was awesome. I gave it an Infiltration promotion, so it became my "Ninja Tank." Eventually, you'll find the Lost City of Atlantis, and score about 6+ techs for free. Like I said, exploration is important.
I've started to try for an economic victory, but I haven't quite figured out how to make gold in the city early on. That makes it tough.