Cellular membranes such as the plasma membrane are complex organelles composed of phospholipids, sterols and proteins, among others. The spatial organization of these components is an important factor that affects biological function. Our work uses computer simulations and mathematical modeling to study the emergence of spatial order in two specific applications: the phase behavior of multicomponent lipid bilayers and the effect of membrane- induced interactions on membrane-bound proteins. Composition heterogeneities in model membrane systems have attracted much attention recently as they might form the basis for lipid rafts, small domains rich in sterols that corral membrane proteins. We study the phase behavior of multicomponent bilayers using simulations of coarse-grained molecular and general field-theory based models. We find a wide range of membrane systems that exhibit composition correlations over nanometer length scales, which provides new insight into the formation of spatial inhomogeneities in membranes. The binding of proteins to cellular membranes imposes local constraints on the membrane’s geometry. This gives rise to an interaction between these proteins that is transmitted by the membrane’s elastic behavior. We develop a hybrid model that combines a continuum description of the membrane with a particle representation of the proteins. We show that the membrane-induced interaction gives rise to an effective attraction between proteins, which occurs over length scales much larger than typical intermolecular forces.