The fundamental physical principles of the lateral organization of trans-membrane proteins and peptides as well as peripheral membrane proteins and enzymes are considered from the point of view of the lipid-bilayer membrane, its structure, dynamics, and cooperative phenomena. Based on a variety of theoretical considerations and model calculations, the nature of lipid-protein interactions is considered both for a single protein and an assembly of proteins that can lead to aggregation and protein crystallization in the plane of the membrane. Phenomena discussed include lipid sorting and selectivity at protein surfaces, protein-lipid phase equilibria, lipid-mediated protein-protein interactions, wetting and capillary condensation as means of protein organization, mechanisms of two-dimensional protein crystallization, as well as non-equilibrium organization of active proteins in membranes. The theoretical findings are compared with a variety of experimental data.