I will discuss a connection between certain Khovanov- and Heegaard Floer-type invariants for knots, braids, and 3-manifolds. Specifically, I will explain how the bordered Floer homology bimodule associated to the branched double-cover of a braid is related to a similar bimodule defined by Khovanov and Seidel. This is joint work with Denis Auroux and J. Elisenda Grigsby.