  Almost all investigations of turbulent flows in academia and in the industry
utilize some degree of turbulence modeling. Of the available approaches to
turbulence modeling Reynolds Stress Models have the highest potential to
replicate complex flow phenomena. Due to its complexity and its importance in
flow evolution modeling of the pressure strain correlation mechanism is
generally regarded as the key challenge for Reynolds Stress Models. In the
present work, the modeling of the pressure strain correlation for complex
turbulent flows is reviewed. Starting from the governing equations we outline
the theory behind models for both the slow and rapid pressure strain
correlation. Established models for both these are introduced and their
successes and shortcomings are illustrated using simulations and comparisons to
experimental and numerical studies. Recent advances and developments in this
context are presented. Finally, challenges and hurdles for pressure strain
correlation modeling are outlined and explained in detail to guide future
investigations.
