What are elephants closely related to?

Close elephant relatives like the extinct mammoths and mastodons belong to the group Proboscidea (which basically means "nose-havers", in reference to the trunk).

This group is contained within the wider group Afrotheria --see https://en.wikipedia.org/wiki/Afrotheria -- a group with surprising contents including elephant shrews, aarvarks and (among the groups most closely related to elephants) manatees!