Elephant’s Winter Joy. Elephants play in the snow at a zoo in Berlin. Elephants are large land mammals in two genera of the family Elephantidae: Elephas and Loxodonta. Three species of elephant are living today: the African bush elephant, the African forest elephant and the Asian elephant . All other species and genera of Elephantidae are extinct, some since the last ice age although dwarf forms of mammoths may have survived as late as 2,000 BC. Elephants and other Elephantidae were once classified with other thick-skinned animals in a now invalid order, Pachydermata.