We used computer simulations to study the effect of phase separation on the properties of lipid monolayers. This is important for understanding the lipid-lipid interactions underlying lateral heterogeneity (rafts) in biological membranes and the role of domains in the regulation of surface tension by lung surfactant. Molecular dynamics simulations with the coarse-grained MARTINI force field were employed to model large length (similar to 80 nm in lateral dimension) and time (tens of microseconds) scales. Lipid mixtures containing saturated and unsaturated lipids and cholesterol were investigated under varying surface tension and temperature. We reproduced compositional lipid demixing and the coexistence of liquid expanded and liquid-condensed phases as well as liquid ordered and liquid disordered phases. Formation of the more ordered phase was induced by lowering the surface tension or temperature. Phase transformations occurred via either nucleation or spinodal decomposition. In nucleation, multiple domains formed initially and subsequently merged. Using cluster analysis combined with Voronoi tessellation, we characterized the partial areas of the lipids in each phase, the phase composition, the boundary length, and the line tension under varying surface tension. We calculated the growth exponents for nucleation and spinodal decomposition using a dynamical scaling hypothesis. At low surface tensions, liquid ordered domains manifest spontaneous curvature. Lateral diffusion of lipids is significantly slower in the more ordered phase, as expected. The presence of domains increased the monolayer surface viscosity, in particular as a result of domain reorganization under shear.