  Bordered Floer homology is an invariant for 3-manifolds with boundary,
defined by the authors in 2008. It extends the Heegaard Floer homology of
closed 3-manifolds, defined in earlier work of Zolt\'an Szab\'o and the second
author. In addition to its conceptual interest, bordered Floer homology also
provides powerful computational tools. This survey outlines the theory,
focusing on recent developments and applications.
