A review of the current status of computation of turbulent impinging jet heat transfer is presented. It starts with a brief introduction to flow and heat transfer characteristics of jet impinging flows considering the simplest jet impinging geometry: normal impingement of a single jet into a flat surface. Subsequently, a review of recent computational studies related to the same geometry is presented. The effects of different subgrid scale models, boundary conditions, numerical schemes, grid distribution, and size of the computational domain adopted in various large eddy simulations of this flow configuration are reviewed in detail. A review of direct numerical simulation of the same geometry is also presented. Further, some recent attempts in Reynolds-averaged Navier-Stokes modeling of impinging flows are also reviewed. A review of computation of other complex impinging flows is also presented. The review concludes with a listing of some important findings and future directions in the computation of impinging flows.