Turbulent flows play a crucial role in various engineering and scientific applications, and the accurate prediction of these flows remains a challenging task. This review explores the application of the Shear Stress Transport Scale-Adaptive Simulation (SST-SAS) turbulence model for solving incompressible turbulent flows, with a specific focus on unsteady wakes behind bluff bodies. Providing a concise overview of the model's formulation and its advantages, this article highlights the efficacy of the SST-SAS model in simulating the intricate dynamics in different configurations of circular cylinders. The present study affirms that the SST-SAS model can be considered a highly viable alternative for simulating unsteady flows around bluff bodies due to the good predictive quality of the resulting simulations.