This paper is concerned with the application of two different simulation approaches for turbulent flows, namely large eddy simulation (LES) and direct numerical simulation (DNS). Due to steadily increasing computer power and memory both methods have become attractive alternatives to classical turbulence modeling based on the Reynolds- averaged Navier-Stokes equations (RANS) combined with statistical turbulence models to close the system of equations. Based on two different examples, the flow past a circular cylinder at sub-critical Reynolds numbers and the turbulent flow inside a stirred vessel, the paper summarizes the ongoing research on LES and DNS at the LSTM Erlangen. The cylinder flow was computed by LES in order to validate the applied physical models and the numerical methods based on a well-documented test case involving remarkably complex flow features in the direct vicinity and the wake of the cylinder. Based on the results for two different Reynolds numbers the potential as well as some deficiencies of the LES approach for practically relevant turbulent flows are discussed. The DNS technique was employed for a quite complex time-dependent geometrical configuration given by a closed vessel equipped with four baffles and stirred by a six blade Rushton turbine. Computations of the stirred vessel flow were carried out for a wide range of Reynolds numbers, including laminar and turbulent regimes. Results of important integral parameters such as the Newton number show a good agreement with experimental measurements. The DNS results are compared with RANS predictions to demonstrate the applicability of DNS to complex turbulent flows and its advantages.