In this paper a review will be presented on the application of Computational Fluid Dynamics (CFD) to the field of Chemical Reaction Engineering (CRE). After a brief introduction and explanation of the traditional approaches followed within the field of CRE, the CFD discipline and its historical development will be briefly discussed. Some important areas of application will also be mentioned. Subsequently the theoretical framework will be expanded on and the techniques involved in the numerical solutions will be briefly outlined. Throughout this paper the authors have found it useful to make a distinction between i) Single Phase systems and ii) Multiphase Systems. In our review a brief section has been incorporated on experimental validation which is considered to constitute a critical action to pave the way for more widespread acceptance of CFD in the chemical engineering community, especially in connection with multiphase now applications. The authors have used this opportunity to present some of the results which have been obtained during their own research activities. Finally some recommendations for future actions will be given.