Summary: A general classification of two-phase flows and a number of possible ways to formulate two-fluid models are discussed. The two-fluid model is adopted, and a general procedure to develop such a model is presented. The local instantaneous equations of mass and momentum are derived together with the corresponding jump conditions. Volume, time and ensemble averaging procedures are discussed, and averaged equations and jump conditions are derived using a general averaging operator. A Reynolds decomposition and weighting procedure is applied to obtain the final equations. The equations necessary to close the system, so-called closure laws, are discussed. The mechanisms contributing to the viscosity of both phases and mixture viscosity models are presented. The particle pressure is discussed, and some simple models based on the modulus of elasticity concept are given. The interfacial momentum transfer term is discussed in detail, and a study of common models of the drag function is presented. A discussion of turbulence models for the gas and particulate phases is included. A summary and critical assessment of published work on simulations of hydrodynamics in bubbling and circulating fluidized beds are also presented.