The transitional region downstream of the nozzle exit in wall jets over plane and curved surfaces at high Reynolds numbers (Rej=10,000) is investigated using three-dimensional Navler-Stokes simulations. The transition process is crucial for the development of the turbulent wall jet since it leaves a strong signature farther downstream. During transition, energetic vortical structures (spanwise, streamwlse) develop from hydrodynamlc instabilities and propagate into the turbulent now, while strongly influencing the meannow characteristics, e.g., the spreading rate, the skin-friction, and ultimately the separation location. Smaller-sized Navier-Stokes simulations are employed for investigating the influence of various now parameters, such as the shape of the jet profile at the nozzle exit, the disturbance level, and also the effect of wall curvature on the overall development of the vortical structures and the mean now. For some flow configurations, the transition mechanisms are investigated in greater detail using Direct Numerical Simulations with a grid-resolution that is fine enough for capturing the transition mechanisms during the later stages of the breakdown. The simulations show that the development of spanwise vortices during wall-jet transition leads to the formation of braid vortices that loop around the spanwise vortices and appear as streamwise vortices in the time-averaged now. In the presence of wall curvature (Coanda wall jet), the strength of the spanwise vortices is strongly reduced and streamwise vortices develop instead from a centrifugal Görtler-tpye instability.