Clan relationships in Six Ages are complex.
Your neighbors will judge you by your actions. Generosity may win friends; successful raids may earn both dislike and fear. Success at rituals helps your reputation; failure harms it.
And of course, cultural and religious differences are sure to complicate matters.
Like and Dislike[]
Naturally, your neighbors can like or dislike you. This is indicated on the map with the color of their names: pink indicates dislike, light purple neutrality, and dark purple friendliness. Allies are shown in blue and enemies in red.
You can help your relationship with a given clan by giving gifts to them, although this isn't a cure-all. If you marry a prominent woman of your clan into another, you'll also find that your relationship with this clan gradually increases.
Fear and Mockery[]
Some of your neighbors take you seriously; others don't. This is largely independant of how much the clan in question likes you, although friendly clans will "respect" rather than fear you. It's possible to have a friendly clan that mocks you and an enemy that fears (respects) your might, or the other way around.
Both military victories and ritual success will increase other clans' fear of you; wait to long between raids, or fail in rituals, and they'll mock you.
Allies[]
Allies, or sworn friends, are extremely useful to have. Allies allow you to support more temples, because allies worship together. Your allies will also sometimes warn you of attacks. You can even ask an ally to lend you warriors for a raid--but their agreement is not guaranteed. Even a loyal ally may demand that you pay back the favors you owe before asking them to risk their lives for you. Allies will always like you, and it's easier to ally with a clan that likes you already. Of course, respect is also useful: if your military might is great enough, you may find other clans come to you to propose alliance. You can gain allies by Requesting An Alliance, and during the game other clans may also come to you asking for an alliance, particularly if you've been having great military success.
Allies are useful, but you can't maintain infinite alliances. At the beginning of the game, you can handle only three before your allies start to worry that you won't be able to handle your commitments to them. This limit can be raised by sending out emissaries: once you've sent an emissary to every clan of a given culture, you'll be allowed an extra alliance, and sending emissaries to every single clan will allow one more alliance as well. If you make more alliances than recommended some clans may request you sever an alliance. Sometimes they can be convinced to remain allies if you just gift them instead.
It is possible to make alliances with clans that hate you to reduce them harming you. They will be listed as Liking you afterwards though they can still decide to herd Raid you. On rare occasions they may even go on a Raid against you, but alliances largely shut down Raids.
Successfully demanding tribute from an ally can cause them to break off their alliance with you. Attacking an ally to break up an alliance can cause you to lose magic otherwise.
Feuds[]
Feuds are essentially wars declared between clans. A clan you're feuding with will raid you, whether they fear or mock you.
Feuding clans will often refuse to see your emissaries, so if you're trying to send an emissary to all clans of a given culture, make sure to do that before you start any feuds.
Emissaries[]
You can send emissaries to other clans to call in favors, give gifts, propose alliances, or resolve feuds.
Giving gifts can make other clans like you more, with larger gifts having a greater effect. This isn't a cure-all, though; the gift doesn't erase the memory of past slights. And gifting clans can also make them fear you less.
Sending an emissary to every clan of a given culture gives you certain benefits—most tangibly, it raises the alliance cap by one. So you may wish, for example, to visit all the Wheels in the game before moving onto the Rams. And keep in mind that a clan you're feuding with may attack your emissaries rather than accepting their visit!
You'll want to send emissaries periodically; fail to do so for too long and other clans will start to become suspicious of you and to doubt your commitment to diplomacy.