Given a (decorated) link cobordism between two links K and L (that is, an embedded surface in S^3 x [0,1] that K and L co-bound), Juhász defined a map between their link Floer homologies. We prove that when the surface is an annulus the map preserves the natural bigrading of HFL and is always non-zero. This has some interesting applications, in particular the existence of a non-zero element in HFL(K) associated to each properly embedded disc in B^4 whose boundary is the knot K in S^3.  I will then discuss some properties of the map in HFL when the cobordism is not necessarily given by an annulus.  This is joint work with András Juhász.