Swans belong to the genus Cygnus and the family Anatidae, which also includes geese and ducks. Swans are grouped with the closely related geese in the subfamily Anserinae where they form the tribe Cygnini. Swans usually mate for life, though 'divorce' does sometimes occur, particularly following nesting failure.

Mute Swan, Cygnus olor
Black Swan, Cygnus atratus of Australia, and introduced in New Zealand.
Black-necked Swan, Cygnus melancoryphus
Whooper Swan, Cygnus cygnus breeds in Iceland and subarctic Europe and Asia, migrating to temperate Europe and Asia in winter.
Trumpeter Swan, Cygnus buccinator is the largest North American swan. Very similar to the Whooper Swan
Tundra Swan, Cygnus columbianus is a small swan which breeds on the North American tundra, further north than Trumpeter Swan. It winters in the USA.
Bewick's Swan, Cygnus (columbianus) bewickii is the Eurasian form which migrates from Arctic Russia to western Europe and eastern Asia (China, Japan) in winter.