The two-dimensional phase diagram of phospholipid monolayers at air-water interfaces has been constructed from Langmuir compression isotherms. The coexistence region between the solid and fluid phases of the monolayer ends at the critical temperature of the transition. The small-scale lateral structure of the monolayers has been imaged by atomic force microscopy in the nm to mu m range at distinct points in the phase diagram. The lateral structure is immobilized by transferring the monolayer from an air-water interface to a solid mica support using Langmuir-Blodgett techniques. A transfer protocol that ensures preservation of the structure during the transfer has been established. The lateral structure reflecting the density fluctuations has been visualized and quantitatively characterized as the monolayer passes through a series of first-order phase transitions and ultimately approaches a critical point. The critical behavior inferred from the thermodynamic as well as the structural data is found to be consistent with the 2D Ising universality class. Additional results are presented demonstrating the presence of striped phases and coexisting domains in binary mixtures.