To execute their many vital functions, cell membranes are highly organized. Here, we review how membrane structure shapes signal transduction across membranes. Recent experimental and computational advances have shed significant light on mechanisms linking the function of membrane signaling proteins to the composition and physical properties of the membrane lateral structures in which they are embedded. We provide an overview of the structural characteristics of membranes containing heterogeneous mixtures of lipids and other molecules and summarize work on "raft" domains in model and cell membranes, as determined by microscopy, spectroscopy, neutron scattering, and computer simulations. We discuss the principles of partitioning of proteins into membranes and how the structure, dynamics, and function of membrane-embedded and peripheral proteins can be modulated by specific membrane components and physical properties of membranes and raft domains. Finally, we discuss challenges and future directions toward a molecular-level understanding of how membrane organization gives rise to various context-dependent cellular signaling.