Non-equilibrium systems that are in a dynamic interaction with their environments can lead to the emergence of complex phenomena. Such "active" systems have been investigated in the context of classical statistical physics and biophysics. However, experimental advances have now made it possible to engineer similar types of system in regimes where quantum mechanical effects become important. Such systems can exchange energy and information with their environment in a way that leads not only to dissipation and decoherence but also to feedback loops that steer the system towards interesting quantum states. In particular, active systems can feature new phases of matter that differ from any existing phase in equilibrium. Understanding the possibilities in this realm and their underlying theoretical principles is still in its early stages. The PhD candidate's research will contribute to this effort by adapting various techniques from equilibrium quantum statistical mechanics to the non-equilibrium setting, by constructing simple examples of such active quantum systems and by studying their behavior in numerical experiments.