Due to the multiscale nature of two-phase flows, high-order methods are an essential tool to gain further understanding of droplet dynamics phenomena. However, the construction of robust and accurate high-order schemes is a challenging process due the lack of a stabilization mechanism. This is especially the case when compressible fluids are considered, for which discontinuities in the solution might occur and a complex interaction between fluid flow and thermodynamics is present. In the present work, recent results of our numerical framework for compressible droplet flows are presented. The numerical method is based on the high-order discontinuous Galerkin spectral element method and includes both a sharp and a diffuse interface approach. We investigate the parallel performance of our scheme in the most challenging case and consider several applications that include typical interfacial flow phenomena, e.g., evaporation and droplet collisions.