We will survey some results on the first order theory of free groups and free products of groups, and indicate concepts and techniques from low dimensional topology that play an essential role in proving, and at times even stating, some of these results. These will include Tarski's problem on the elementary equivalence of non-abelian free groups, and Vaught-Malcev problem on the elementary equivalence of free products of pairs of elementarily equivalent groups, as well as other results on the structure of definable sets in related theories. We will assume no prior knowledge in model theory nor in low dimensional topology.