Shock wave turbulent boundary layer interactions can occur in both internal and external supersonic flows. Accurate predictions of the associated unsteady aerothermal loads would allow for lighter or more efficient designs. Such predictions have to be grounded in a detailed understanding of the underlying flow physics. Simulations that reveal the unsteady fluid dynamics can contribute to the physical understanding. Large-eddy simulations and hybrid turbulence model simulations of unswept and swept interactions were carried out for momentum thickness Reynolds numbers at separation of approximately 1,000 and 4,000. The simulations reveal a low-frequency unsteadiness at separation and a broad-band high-frequency unsteadiness at reattachment. Pronounced “bulges” of the separation shock are observed for the hybrid simulations of the unswept interaction at the higher Reynolds number. The wavelength of the “bulges” appears to scale with the width of the near-wall streaks. When a freestream crossflow component is added to simulate an infinite swept interaction, the “bulges” disappear. Simulations of a finite swept interaction display conical symmetry and spanwise structures in the interaction region that are slowly traveling away from the symmetry plane.