Computational Fluid Dynamics (CFD) and its applications have developed quite rapidly during the last ten years. This fast growing hybrid branch of Mechanics and Mathematics is certainly to be considered as a potentially useful and efficient tool in the field of Chemical Engineering and more specifically in the area of Chemical Reaction Engineering (CRE). The difficulties in this new approach stems from the consequence of the complexity of the mechanims to be simulated simultaneously: fluid dynamics, chemical reactions and physical aspects of each system considered. Another difficulty comes from the numerical treatment of the equations for the final model, resulting in very sophisticated and diversified mathematical treatments. The types of chemical reactors to be considered for potential performance improvements when applying CFD as a new tool for their design are numerous; two broad classes of problem have be identified as relevant to this new approach: (a) Systems involving fast chemical reactions, with characteristic times of the same order of magnitude as the characteristic time scales of turbulence. In-line mixing equipment should preferably be studied for this type of reactions. (b) Multiphase systems, whose scaling-up still has to be performed with great difficulty and, more often than not, according to empirical procedures based on very simplified models. When looking at the various types of systems found in practice, it appears that gas-liquid and fluid-solid systems should be considered first. However, basic knowledge is still missing concerning the physical behaviour of these systems, especially for the coalescence of bubbles and the momentum transfer between gas and solid. Specific research should be done in order to get this missing information. Presently there are a certain number of existing CFD software packages available commercially or developed by various research laboratories. This is certainly an interesting starting point, but we can never be sure that the numerical results given by any of these software packages are applicable to a practical industrial case, without checking these results in one way or another. There is quite general agreement on the necessity of obtaining experimental data concerning problem examples, in order to check and compare the computation results of the various software packages proposed for dealing with these specific problems. On the experimental side, there are a great deal of measurement methods able to give local values of temperature, pressure, velocities, concentrations of chemical species, phases ratio, size of bubbles, drops or particles, as well as to produce an overall visualization of flows. We have mentioned the difficulties linked to the mathematical treatment of the equations written for simulating reactive flows. As usually done in CFD, for most problems encountered, a first useful solution can be obtained by limiting the model to one or two space dimensions (1D or 2D). However, very often it will be necessary not only to solve the 3D simulation set of equations, but also to achieve the unstationary solution of the same equations in order to really represent the true behaviour of the physical system. This last objective means much more complicated reserach, especially from the mathematical point of view.