Heegaard Floer homology was developed as an extension of the Seiberg-Witten invariant of closed 4-manifolds to closed 3-manifolds and 4-manifolds with boundary, in the style of topological field theories. As originally conceived, Bordered Heegaard Floer homology is a further extension of the simplest version of Heegaard Floer homology to 3-manifolds with boundary. In this talk, we will survey the formal structure of bordered Heegaard Floer homology, applications to topology, and connections to other fields.