Lipid bilayers constitute the basis of biological membranes. Understanding lipid mixing and phase behavior can provide important insights into membrane lateral organization (the "raft" hypothesis). Here we investigate model lipid bilayers below and above their miscibility transition temperatures. Molecular dynamics simulations with the MARTINI coarse-grained force field are employed to model bilayers on a length scale approaching 100 nm and a time scale of tens of microseconds. Using a binary mixture of saturated and unsaturated lipids, and a ternary mixture of a saturated lipid, an unsaturated lipid and cholesterol we reproduce the coexistence of liquid-crystalline and gel, as well as liquid-ordered and liquid-disordered phases. By raising the temperature or adding hybrid lipids (with a saturated and an unsaturated chain), we induce a gradual transition from a two-phase to a one-phase state. We characterize the evolution of bilayer properties along this transition. Domains of coexisting phases change to dynamic heterogeneity with local ordering and compositional de-mixing. We analyze the structural and dynamic properties of domains, sizes and lifetimes of composition fluctuations, and calculate the in-plane structure factors.