Summary: In his solution to the Tarski problem, Sela developped geometric tools to show that all free groups of finite rank are elementary equivalent, and gave a full description of finitely generated models of their common theory (which need not be free). We are interested in types of elements in these groups, and in particular in the type of primitive elements of the free groups (elements which are part of a basis). A result by Pillay implies that any element of a free group which has the same type (i.e. which satisfies the same first order formulas) as a primitive element is itself primitive. In joint work with Sklinos, we gave a characterization of elements realizing this type in other (i.e. not necessarily free) finitely generated groups elementary equivalent to free groups (an important example of such models are the fundamental groups of closed surfaces). This description of a very geometric nature is closely related to the description of elementary subgroups of such groups. We also deduce from this that most surface groups are not homogeneous.