A group G is said to be homogeneous if any two finite tuples of elements of G that have the same type are in the same orbit under the action of the automorphism group of G. Ould Houcine and Perin - Sklinos proved that finitely generated free groups are homogeneous, but the situation is completely different in the presence of elements of finite order. In this talk, I will present some results on homogeneity of virtually free groups and (hyperbolic) Coxeter groups (a nice class of groups generated by involutions). This is based partly on joint work with Gianluca Paolini.