We present a microscopic theory of transport through quantum dot setups coupled to superconducting leads. We derive amaster equation for the reduced density matrix to lowest order in the tunneling Hamiltonian and focus on quasiparticle tunneling. For high enough temperatures transport occurs in the subgap region due to thermally excited quasiparticles, which can be used to observe excited states of the system at low bias voltages. On the example of a double quantum dot we show how subgap transport spectroscopy can be done. Moreover, we use the single level quantum dot coupled to a normal and a superconducting lead to give a possible explanation for the subgap features observed in the experiments of Dirks, Chen, Birge, and Mason [Appl. Phys. Lett. 95, 192103 (2009)].