Successful reactor engineering crucially depends on the ability to predict and control the fluid dynamics and mixing occurring in industrial reactors. Computational fluid dynamics (CFD) offers the possibility of predicting the detailed flow and turbulence characteristics of the reactor under different geometrical and operating conditions. In this review, we have focused on CFD methods for simulating recirculating, turbulent single and two phase flows in reactors. An attempt has been made to convey and clarify the potential of CFD for reactor engineering research. The emphasis is on informing the reader about different aspects of constructing CFD simulation models of reactors rather than an exhaustive literature review. Formulation of transport equations for flow modelling is discussed for single and dispersed two phase flows. A framework of two fluid models and the formulation of phase interaction terms is discussed. Two equation turbulence models which are most likely to be used to simulate flow in reactors are discussed in detail. Numerical techniques and algorithms for solution of these transport equations are reviewed. Flow simulations of the two most commonly used reactors, namely the stirred tank reactor and tile bubble column reactor, are discussed in detail. In a stirred tank reactor, the flow around the rotating impeller blades interacts with the stationary baffles and generates a complex, three-dimensional turbulent flow. In a bubble column reactor, in which reactant gas (along with an inert gas if present) itself provides the required stirring action, local flow, turbulence and gas holdup distribution are interrelated in a complex way. Different approaches and attempts to simulate these complex circulating flows are critically reviewed. The limitations of the present state of knowledge with respect to possible applications in reactor engineering are discussed. Some suggestions for further research are offered.