Disparate biological processes involve fusion of two membranes into one and fission of one membrane into two. To formulate the possible job description for the proteins that mediate remodeling of biological membranes, we analyze the energy price of disruption and bending of membrane lipid bilayers at the different stages of bilayer fusion. The phenomenology and the pathways of the well-characterized reactions of biological remodeling, such as fusion mediated by influenza hemagglutinin, are compared with those studied for protein-free bilayers. We briefly consider some proteins involved in fusion and fission, and the dependence of remodeling on the lipid composition of the membranes. The specific hypothetical mechanisms by which the proteins can lower the energy price of the bilayer rearrangement are discussed in light of the experimental data and the requirements imposed by the elastic properties of the bilayer.