Let G be a flnite abelian group. A sequence in G is barycentric if it contains one element \average of its terms. We give a survey of results and open problems concerning su‐cient conditions for the existence of barycentric sequences. Moreover values and open problems on the k-barycentric Davenport constant BD(k;G), the barycentric Davenport constant BD(G), the strong k-barycentric Davenport constant SBD(k;G) and barycentric Ramsey numbers BR(H;G) for some graphs H are presented. These constants are related to the Davenport constant D(G).
