Computational Fluid Dynamics (CFD) involves the numerical solution of conservation equations for mass, momentum and energy in a flow geometry of interest, together with additional sets of equations reflecting the problem at hand. In this paper the current capabilities of CFD for chemical reactor engineering are illustrated by considering a series of examples from industrial practice. These examples form the basis for the identification of future trends and potential stumbling blocks. Recent progress in the predictions of flow in baffled stirred tank reactors is reviewed. Improved turbulence modelling and high-performance computing have a particularly important part to play in the future applications of CFD to this type of reactor. In the next example, which concerns non-Newtonian, non-isothermal flow in an extruder, CFD turns out to be helpful in understanding the role of temperature profiles and residence time distribution in determining the product quality. In this application area limitations in available computing power and experimental validation of rheological models are both important. CFD simulations of gaseous turbulent flow with competing parallel and consecutive reactions constitute the third example. Apart from the need for accurate kinetic rates, the main problem in this case is the optimal choice of closure of chemical source terms in the mean transport equations for species mass fractions. Several models have been implemented in a commercial CFD code and validated with plant data, thus allowing CFD model calculations to contribute to an improved reactor design. Finally, a discussion of future needs and expectations of the chemical processing industry with respect to CFD modelling, mainly focussing on multiphase flow, is given.