Shock-wave/turbulent boundary layer interactions (SBLIs) are a typical hallmark of high-speed aerodynamics. Common examples of SBLIs can be found both in external flows, such as transonic/supersonic airfoils, wing-body junctions, aircraft control surfaces, and in internal flows such as engine supersonic inlets, compressors and turbines [1]. More broadly, SBLIs occur whenever a shock wave encounters a turbulent boundary layer developing on a solid surface. The impact of a shock on a boundary layer typically results in substantial flow separation, which can lead to significant decreases in performance. This chapter concentrates on the numerical aspects of SBLIs. In the first part, we elucidate the numerical framework utilized to simulate these interactions using Direct Numerical Simulations (DNS), both in Cartesian and curvilinear coordinates. Special emphasis has been placed on the handling of convective terms, which have been reformulated into a convenient split form ensuring the discrete preservation of total kinetic energy. Following this, the chapter presents qualitative and quantitative outcomes from a classical time-reversibility test. Subsequently, it delves into a more practical scenario, detailing the results of a fully turbulent supersonic compression corner.