This thesis reports on a numerical study of a round, isothermal turbulent jet of incompressible fluid, impinging normally on a flat wall at a different temperature. The aim was to generate detailed information about the ime-dependent three-dimensional velocity and temperature field, and, based on this, to extract statistically averaged flow and turbulence properties, as well as to identify and analyze the dominant vortical structures, their evolution and thermal signature on the target wall. The main body of the thesis deals with LES studies using the dynamic subgrid-scale model, of flow and heat transfer in a round impinging jet at Re=20000 and orifice-to-plate distance h/D=2. The LES were performed using the in-house unstructured finite-volume computational code T-FlowS. Prior to the jet simulations, the computational code and its features (the numerical schemes and solver, boundary conditions, mesh generation and refinement, implementation of the dynamic sub-grid scale model into an unstructured code) as well as structure identification and interpretation, were tested in the simulation of a plane channel and a pipe flow, the latter with heat transfer. Because a round impinging jet contains several flow regions, each featured by different flow physics (free jet expansion, impingement, jet deflection with strong acceleration, radially spreading and decelerating wall jet), several mesh refinements (with up to 10 million mesh cells), and different conditions at the free inflow boundary of the computational domain were explored until satisfactory agreement with the available experimental results was achieved. The final results, believed to be credibly accurate, were processed to extract the mean flow and turbulence statistics, budgets of the transport equations for the Reynolds stresses and turbulent-heat-flux components, as well as to analyze the time dynamics of the vortical structure and its relation with the instantaneous and averaged wall heat transfer. The LES confirmed some of the experimentally detected features such as a dip and a second maximum in the Nusselt number and negative production of turbulence kinetic energy in the stagnation region, but also revealed some other interesting phenomena such as strong oscillation of the stagnation point and the unsteady flow separation at the onset of wall-jet formation. These events were identified as the main cause of the Nu-number nonuniformity, and were linked to the ring vortices generated in the jet shear layer, and their asymmetric break-up prior or after the impingement. The second focus of the thesis was the study of the feasibility of combining the LES and RANS approaches into a hybrid method. The goal was to provide the time resolved three-dimensional solutions of the velocity and temperature field (though associated with the larger turbulence scales only) while using the mesh size typical of that used in off-wall LES or in the RANS computation. Two directions were pursued in parallel: zonal approaches with predefined RANS and LES zones, and seamless methods with a single statistical model serving both as the RANS- and as the LES sub-grid scale model. Prior to hybrid simulations, several RANS models were tested in computation of several generic flows with heat transfer, aimed at examining their suitability to serve as the near-wall RANS model in hybridization with LES. In order to verify the hybrid approaches, simulations of the plane channel flow at a range of Reynolds numbers have been carried out with four different hybrid models. Two of the hybrid models tested were subsequently applied to simulate the round impinging jet having the same Re number and configuration as in the LES study, but using much coarser grid ($\approx $ 1.6 million). While the hybrid simulations yielded satisfactory results in plane channel flows, their performance in the impinging jet - though superior to the conventional LES when using the same (coarse) mesh, was not fully satisfactory. Several critical issues have been detected requiring further testing that was beyond the scope of this thesis, thus preventing the final conclusions to be drawn. Based on this research, some directions for further research both in hybrid LES/RANS and in conventional LES have been proposed.