The use of wall-modeled large-eddy simulation (WMLES) is explored in the context of compressible flows with a focus on cold-wall boundary layers and flows with shock-induced separation. It is observed that for cold-wall flows, a "mixed" scaling for the length scale appearing in the eddy viscosity formulation outperforms the classical semilocal scaling for obtaining predictions of heat flux and skin friction. A few shock/boundary-layer interaction (SBLI) cases are examined in some detail, and model modifications are proposed to overcome identified deficiencies. It is shown that using WMLES the low-frequency characteristics of SBLI at high Reynolds number can be quantitatively captured. A dynamically switched version of the equilibrium model is proposed; this shows promise for relatively inexpensive simulations at these conditions.