The paper summarizes current strategies for computing heat transfer coefficients in complex turbulent flows based on numerical solution of the averaged equations for momentum and enthalpy and corresponding equations for averaged properties of the turbulent flow field. It argues that, for accuracy and width of applicability, a fine-grid low-Reynolds-number treatment should be employed near the wall in place of wall functions, despite the attractive simplicity of the latter approach. Several examples are provided that bring out the benefit from adopting second-moment closures, in which attention is focused on the turbulent stresses and heat fluxes themselves rather than on effective viscosities and thermal diffusivities. Directions for future research are briefly discussed, an important contribution to this effort being the direct numerical simulation of the near-wall dynamic and thermal turbulence field.