The sharp-interface resolution of compressible gas-liquid flows is made particularly difficult by the coupling between the hydrodynamics and the thermodynamics, the stiff equation of state in the liquid phase, the need to represent important discontinuities in the fluid properties, and the modeling of complex interfacial phenomena. In this work, a high-order discontinuous Galerkin method with a level-set interface tracking method is used to handle the moving sharp interface. It is combined with multiphase Riemann solvers to impose the physical jump compatibility relations, with the possibility of modeling phase transition effects. The proposed approach is then tested on some verification test cases showing its potential for future applications.