Flow separation is always three-dimensional despite the fact that most of the past research has focused on two-dimensional separation. The three-dimensional character of separation is particularly relevant when low-aspect ratio geometries are considered. Separation is often associated with unsteadiness, which is caused by large coherent structures that are a consequence of hydrodynamic instability mechanisms of the mean-flow. We are employing direct numerical simulations for investigating the highly-complex flow physics of three-dimensional laminar separation bubbles. The introduction of pulse disturbances allows us to probe the instability mechanisms. In parallel, we are also employing hybrid turbulence models for simulations of the turbulent flow through a square-duct, and for the Stanford University asymmetric diffuser experiments. By advancing the understanding of the fundamental mechanisms governing three-dimensional separation and by devising modeling strategies for high-Reynolds number flows, we are laying the foundation that may lead to better predictive tools and to separation control devices for practical applications.