String topology (defined by Chas and Sullivan) is the study of the topology of the space of loops (or strings) in a manifold. Chas and Sullivan's work, as well as recent work by Cohen, Jones, Godin, and others focuses on defining various algebraic operations on the space of loops (or its homology). One can phrase many of these constructions in the language of field theories used by physicists (though our approach will be purely mathematical). I'll give an introduction to these sort of field theories from the point of view of algebraic topology, and explain how various flavors of string topology fit into this framework.