As a lover and critic of the strategy genre, I will tell you that this is easily one of my favourite games.
A fairly simple yet addicting game, you start out by choosing which civilization you want to lead to worldwide domination. There are many to choose from, each with different benefits that pile on throughout the ages. There are always three other civilizations chosen at random to face off against. There is also the choice of playing on a certain terrain or with certain conditions or restrictions to achieve victory.
The strategy involved in this game is really remarkable when you think about it. There are four ways to win, and I'm sure you've heard them by now (Domination, Technology, Cultural, Economic). You will find that each civilization is suited more for some victories than others. Choosing the right civilization is key to your success in the harder difficulties.
I liked the civilopedia too. Very nice addition that gives the background for everything that is found in the game.
Things I wish were better: More options with diplomacy, larger armies, possibly more in-depth historical scenarios.
Things I liked: Different difficulties make this game appealing to all audiences, good variety of civilizations to choose from.
Things I loved: Different technology branches and terrain make things interesting, different game scenarios make this an instant "playing this over and over again" game.