Eventually, the influence of religion begins to dwindle (depending on which benefits you've chosen), and you derive most of your income and power from other sources. At this point, Gods and Kings' other major enhancement comes into play: espionage. While spying isn't as fundamental or as critical to success as religion, it is vastly more robust and important than it has ever been in a Civilization game. Spies aren't trained, but are instead awarded at particular intervals throughout gameplay and can be assigned to do everything from stealing technological secrets from rival factions to fomenting a coup d'etat in a city-state and installing a government that's loyal to you.
Spies' missions require a roll of the dice to succeed, but the more successful they are, the more they level up, and the more they level up, the more successful they are. On the other hand, it's also possible for spies to fail, even to the point of causing an international incident and starting a war. Indeed, if caught and interrogated, spies have the potential to reveal secrets about their owners' civilizations, so the espionage game can be risky. Late-game buildings and social policies can affect a civilization's susceptibility to being spied on, but most players will need to take advantage of spies at one point or another to catch up to their rivals.
Ha ha! Take that, 'unmet player!' Later, we found out it was Attila the Hun. Yipes!
Besides religion and espionage, Gods and Kings adds a bevy of new units, buildings, wonders, and civilizations to play. The newly added civilizations bump up the number of female world leaders, and include the semi-mythological Dido, queen of Carthage, and Theodora, empress of the Byzantine Empire. Also included are a bunch of new city-states, including two completely new types: religious ones that boost your faith when you ally with them, and scientific ones that boost your research. On the downside, Gods and Kings doesn't include any of the civilizations or scenarios from previous Civ V expansions, with the exception of the Spanish and the Mongols, the latter of which was free downloadable content anyway.
But that's just about the only thing you can say in the negative about Gods and Kings. Along with all the nifty additions to gameplay and content, AI has been noticeably improved across the board. It no longer puts artillery on the front lines, builds cities right in the middle of someone else's empire, or behaves as if it were schizophrenic in diplomatic negotiations. It's still not perfect, but it's a lot closer than it was before and remains a challenge much further into the late game now. And, depending on how long it has been since you last played Civ V, you'll also notice a slew of gameplay and rule tweaks that help close exploits and loopholes in the rules.
In the end, the best thing you can say about Gods and Kings is that it makes Civ V noticeably more fun--something that anyone who's already familiar with the game would likely say is an impressive achievement indeed.