The quantum spin Hall (QSH) states are novel electronic phases which are characterized by topological invariants rather than by spontaneously broken symmetries. QSH states are distinguished from ordinary insulators by the presence of conducting edge or surface states surrounding an insulating bulk. These protected boundary states were experimentally confirmed in HgTe quantum wells (QW). In this talk, I will present two aspects of transport through a junction between a doped HgTe QW and an s-wave superconductor. First, I will show how Andreev reflection (AR) processes can be used to probe the topological phase of the HgTe QW. Second, I will discuss the existence of a spin Hall effect (SHE) at the interface of the junction and will show how it is related to the coexistence of propagating and evanescent modes at the interface.