In this talk, I will describe multiscale simulation studies into the structure and dynamics of lipid membranes. Membrane structure is the target of intense investigation: new insights into the presence of rafts and microdomains in multicomponent lipid bilayers are frequently reported. Our coarse-grained studies of lipid bilayers revealed surprising features in the lateral structural properties of the bilayer. This finding was verified by atomic-scale studies of large bilayer systems, confirming that coarse-grained models, whose parameters are rigorously derived from more detailed descriptions, can indeed be expected to reproduce the relevant physics and chemistry of the original system. Knowing (transient) membrane structures is a very good starting point. However, since cellular membranes are always under non-equilibrium conditions, understanding their dynamics is at least as crucial. Unfortunately, the dynamics of cell membranes has received considerably less attention than membrane structure, indeed, one could say there is no comprehensive model for membrane dynamics. Even seemingly simple basic dynamic processes, such as the lateral diffusion of lipids in one-component lipid bilayers, are not fully understood. In the second part of my talk, I will describe simulations that have shed new light on the lateral diffusion of lipids.