The law of the wall and related correlations underpin much of current computational fluid dynamics (CFD) software, either directly through use of so-called wall functions or indirectly in near-wall turbulence models. The correlations for near-wall flow become crucial in solution of two problems of great practical importance, namely, in prediction of flow at high Reynolds numbers and in modeling the effects of surface roughness. Although the two problems may appear vastly different from a physical point of view, they share common numerical features. Some results from the ’superpipe’ experiment at Princeton University are analyzed along with those of previous experiments on the boundary layer on an axisymmetric body to identify features of near-wall flow at high Reynolds numbers that are useful in modeling. The study is complemented by a review of some computations in simple and complex flows to reveal the strengths and weaknesses of turbulence models used in modern CFD methods. Similarly, principal results of classical experiments on the effects of sand-grain roughness are reviewed, along with various models proposed to account for these effects in numerical solutions. Models that claim to resolve the near-wall flow are applied to the flow in rough-wall pipes and channels to illustrate their power and limitations. The need for further laboratory and numerical experiments is clarified as a result of this study.