A theoretical study is performed on a microscopic interaction model which describes the transitions between liquid and solid phases of lipid monolayers spread on air/water interfaces. The model accounts for condensation in terms of acyl-chain conformational degrees of freedom as well as in terms of variables which describe the orientations of crystalline domains in the solid. The phase behavior of the model as a function of temperature and lateral pressure is explored using mean-field theory and computer-simulation techniques. Attention is paid to the particular interplay between the two types of condensation processes and effects on the phase behavior due to decoupling of crystalline and conformational order parameters. In the case of decoupling, the model predicts that the high-pressure solid-conformationally ordered phase is separated from the low-pressure liquid-conformationally disordered phase by a liquid-conformationally ordered phase. This prediction is consistent with synchrotron x-ray experiments which show that the chain-ordering transition and the crystallization process need not take place at the same lateral pressure. A characterization is provided of the nonequilibrium effects and pattern-formation processes observed along the isotherms in the phase diagram spanned by lateral pressure and area. A description is given of the kinetics of the nonequilibrium phase transitions and the concomitant heterogeneous microstructure of the monolayer. This leads to an explanation of the peculiarities of the experimentally observed isotherms of lipid monolayer phase behavior. It is pointed out that cholesterol, which promotes lipid-chain conformational order, has a unique capacity of acting as a `crystal breaker' in the solid monolayer phases and therefore provides a molecular mechanism for decoupling crystalline and conformational order in lipid monolayers containing cholesterol. The phase diagram of mixed cholesterol–lipid monolayers is derived and discussed in relation to monolayer experiments. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.