The dynamics of a lipid bilayer membrane is investigated in several different situations. Our model accounts for the transport of lipids along each monolayer, and intermonolayer friction, as well as the membrane fluidity and resistance to bending. First we consider a nearly-spherical vesicle in a shear flow. In this near-spherical limit we can reduce the model to a nonlinear coupled system of equations for the dynamics of the shape and the bilayer density difference. Multiple solution states are found as a function of viscosity ratio and the monolayer slip coefficient. Second, we investigate the stability of a planar membrane subjected to a DC electric pulse. The thin lipid membrane is impermeable to ions and thus acts as a capacitor. A linear stability analysis results in a time dependent system of equations for the growth rate as a function of wave number. Our theoretical findings are relevant to understanding the physical mechanisms of electroporation of biomembranes. Finally we discuss a novel computational method to determine the dynamics of a lipid bilayer vesicle in a viscous flow.