The paper considers issues pertaining to the capabilities and limitations of computational methods for multidimensional turbulent flows of the type encountered in fluids engineering. It argues that CFD, whilst offering considerable predictive power and potential, is not yet sufficiently well established to be applied routinely to complex 3D flows, unless only a rough qualitative. statement is being sought. CFD involves a whole array of ill-defined and ill-understood interacting issues, such turbulence modelling, boundary conditions and the numerical approximation of convection, whose combined influence on predictive realism is never transparent. Illustrative examples are presented to justify the above view. Because of the particular prominence of turbulence modelling as an error source, an indication is provided of current directions in representing turbulence effects by advanced stress/flux closures as a means of improving accuracy. The discussion leads to the conclusion that considerable expertise, physical insight and experience are essential for meaningful solutions to be obtained and for the limitations of computational schemes to be appreciated.