Summary: Impingement and forced convection are preferable methods for cooling gas turbine components. However, influences of various design parameters like crossflow and surface enlargements (like ribs) are not well understood. Thus there is a request for reliable and cost-effective computational prediction methods, due to the experimental difficulties. Such methods could be based on the numerical solution of the Reynolds-averaged Navier-Stokes equations, the energy equation and models for the turbulence field. This paper describes some recent advances and efforts to develop and validate computational methods for simulation of impingement and forced convection cooling in generic geometries of relevance in gas turbine cooling. Single unconfined round air jets, confined jets with crossflow, and three-dimensional ribbed ducts are considered. The numerical approach is based on the finite volume method and uses a co-located computational grid. The considered turbulence models are all the so-called low Reynolds number models. Our recent investigations show that linear and nonlinear two-equation turbulence models can be used for impinging jet heat transfer predictions with reasonable success. However, the computational results also suggest that an application of a realizability constraint is necessary to avoid over-prediction of the stagnation point heat transfer coefficients. For situations with combined forced convection and impingement cooling it was revealed that as the crossflow is squeezed under the jet, the heat transfer coefficient is reduced. In addition, inline V-shaped 45\(^circ\) ribs pointing upstream performed superior compared to those pointing downstream and transverse ribs.