A ribbon concordance is a concordance with only index 0 and  1 handles. In this talk, we will outline a proof that the map on knot  Floer homology induced by a ribbon concordance is injective, and describe some topological applications. We will then describe some further applications to Heegaard Floer invariants of surfaces in 4-manifolds. Parts of this talk are joint with Andras Juhasz, Maggie Miller and Adam Levine.