This document summarizes the three year investigation of transitional and turbulent wall jets using direct numerical simulation (DNS) and large eddy simulation (LES). Towards this end, a three-dimensional, incompressible Navier-Stokes code developed in our research group for DNS of boundary-layer transition was adapted to the wall jet geometry. The code is based on the spatial model and is fourth-order accurate. For the LES, a Smagorinsky based subgrid-scale turbulence model and explicit fourth-order accurate compact filtering were incorporated. As an initial condition, a base flow close to Glauert's similarity solution of the laminar wall jet was employed. This flow was forced by blowing and suction through a slot in the wall. Periodic forcing was used for investigating primary and secondary instabilities in transitional wall jets (Re=2OO) We discovered competing two-dimensional (2-D) and three-dimensional (3-D) instability mechanisms which can be influenced significantly by the type of forcing. 2-D large/amplitude forcing produces (2-D) large coherent structures which reduce wall shear but may lead to ejections of vortices from the wall and even to a detachment of the wall jet. Additional 3-D forcing weakens these coherent structures (especially in the near-wall region) and can thus prevent vortex ejections. In our LES of turbulent wall jets, rapid breakdown to turbulence was triggered by large/amplitude 3-D random forcing. Despite the purely 3-D forcing, 2-D coherent structures still emerge in the free shear layer-like outer region, an indication of the strong 2-D instability of the wall jet. A fully turbulent mean flow which compares well with experiments is obtained for higher Reynolds numbers (Re=2OOO).