Reputation and relations are two different things. Relations with an AI is how much they like you (cautious, gracious, etc.), while reputation is whether or not people will make deals with you. Reputation isn't displayed in game, but you can tell if it's ruined by the fact that no one, even gracious civs, will trade with you anymore (there might be a utility that lets you see your reputation, but I wouldn't know). Reputation can be ruined by breaking trades (either through a declaration of war, or through the trade route being destroyed), breaking peace treaties (declaring war less than 20 turns after making a peace treaty), or declaring war while you have units in their territory.
