Influenza hemagglutinin (HA) is a viral membrane protein responsible for the initial steps of the entry of influenza virus into the host cell. It mediates binding of the virus particle to the host-cell membrane and catalyzes fusion of the viral membrane with that of the host. HA is therefore a major target in the development of antiviral strategies. The fusion of two membranes involves high activation barriers and proceeds through several intermediate states. Here, we provide a biophysical description of the membrane fusion process, relating its kinetic and thermodynamic properties to the large conformational changes taking place in HA and placing these in the context of multiple HA proteins working together to mediate fusion. Furthermore, we highlight the role of novel single-particle experiments and computational approaches in understanding the fusion process and their complementarity with other biophysical approaches.