Cell membranes are fascinating supramolecular aggregates that not only form a barrier between compartments but also harbor many chemical reactions essential to the existence and functioning of a cell. Here, it is proposed to review the molecular dynamics and mosaic organization of the plasma membrane, which are thought to have important functional implications. We will first summarize the basic concepts of Brownian diffusion and lipid domain formation in model membranes and then track the development of ideas and tools in this field, outlining key results obtained on the dynamic processes at work in membrane structure and assembly. We will focus in particular on findings made using fluorescent labeling and imaging procedures to record these dynamic processes. We will also discuss a few examples showing the impact of lateral diffusion on cell signal transduction, and outline some future methodological challenges which must be met before we can answer some of the questions arising in this field of research.