The final type of global activity that takes place in Civilization IV is diplomacy: as leader of your empire, you can sit down with the leaders of other empires and exchange technologies, trade resources or sign treaties. Diplomacy works pretty much the same as in Civ3:
When you first encounter a civ, its leader is added to the list of known contacts (visible in the bottom-right of the screen). At this point you can always contact him/her for one of three actions: negotiate a new deal, declare war, or view (and renegotiate) existing deals [see image on the right]. When negotiating a new deal, or renegotiating an old one, you're taken to a negotation table [see image below]. There you can negotiate a composite deal that is as complex as you'd like: you can offer Gold for an Advance, a City for a World Map, two Resources and an Advance. You can exchange a Resource for an amount of Gold per turn, sign an Open Borders treaty so your Units can pass through each other's territory, demand a City lest you declare war, etc. You can ask a player to declare war with someone else (even if you're not at war with them yourself), or request them to stop an ongoing war.
While you are compiling a proposal, the animated leaderheads will show you with their facial expressions what they think of your proposal. The general attitude they hold towards you, based on both personality and past behaviour, is also visible (Gracious, Polite, Cautious, Annoyed, Enraged, etc). Of course, you're not the only one who can initiate discussions: rival players can make proposals or demands to you as well, including requests to switch your State Religion or Civics to their personal favourites.
Each AI leader has a distinct personality, this is a major area of focus for development for Firaxis. This personality has a major impact on how they behave in diplomacy: Gandhi will be receptive to peaceful players and generous to relatively weak ones, but he will get angry at aggressive players. Genghis Khan on the other hand will shy away from diplomacy altogether, but when he does engage in it he'll be most receptive to warmongers.
This personality does not only cover their behaviour in terms of what they may demand or how active they are in diplomacy, but also in their facial expressions. Each leader has their own set of expressions: they smile when they are happy, frown when they are upset. Some are very expressive while others are constrained. E.g. Hatshepsut is flirtatious, Louis XIV is vain and arrogant. They will be visibly excited when you make them a good deal and they react upset to less favourable proposals. For others, such as Qin Shi Huang, you can only judge their mood by the elevation of their eyebrows. Julius Caesar litterally gives you a thumbs-up or thumbs-down when responding to a proposal.
Civilization IV: Warlords will introduce a new concept to diplomacy: Vassal States. It's not yet known how this will work.
Espionage also exists in Civilization IV and it works pretty much the same as in Civ2: you can build Spy units and send them around the map to infiltrate enemy territory unseen, spy on enemy troop movement, investigate cities, sabotage things, etc -- or use them to expose enemy spies.