Blackadar and Kirchberg introduced the class of matricial field C*-algebras, which are those which approximately embed into finite dimensional matrix algebras. Specializing this property to group C*-algebras, one defies a group to be MF if it admits approximate finite dimensional representations which are approximately faithful and and approximately weakly contained in the left regular representation. I will give a survey of known examples and properties of MF groups, including a recent result showing that free products of amenable groups amalgamated over a common normal subgroup are MF.