An automorphic representation of a group G is said to be distinguished by a subgroup H if it has a nonzero period over H. This notion, introduced by Harder, Langlands, and Rapoport, arises naturally in the study of special cycles on locally symmetric spaces. Twisted relative trace formulae are tools for relating distinction of automorphic representations on different groups. I will introduce these tools and give some applications of them to the study of distinction on unitary groups.