Diverse membrane fusion reactions in biology involve close contact between two lipid bilayers, followed by the local distortion of the individual bilayers and reformation into a single, merged membrane. We consider the structures and energies of the fusion intermediates identified in experimental and theoretical work on protein-free lipid bilayers. On the basis of this analysis, we then discuss the conserved fusion-through-hemifusion pathway of merger between biological membranes and propose that the entire progression, from the close juxtaposition of membrane bilayers to the expansion of a fusion pore, is controlled by protein-generated membrane stresses.