Abstract: We will start by reviewing Morse homology, a version of homology defined in terms of flows, we will discuss the sense in which it is local. We will then see that by considering "flows between flows", one can obtain a more refined invariant of 3-manifolds, called Heegaard Floer homology. We will conclude by discussing recent work with Ozsvath and Thurston on the subtler issue of locality for Heegaard Floer homology.