Circuit quantum electrodynamics (QED) devices typically consist of 'artificial atoms' containing Josephson junctions (JJ) coupled to modes of the electromagnetic field confined within a microwave cavity. Such systems facilitate strong interactions between the microwave electromagnetic field and the artificial atoms, whilst at the same time suppressing decoherence. Circuit QED has already proved an extremely fruitful tool for exploring quantum physics, opening up exciting new avenues of research in areas as diverse as many-body quantum physics, ultra-strong light-matter coupling the production of highly non-classical states and quantum vacuum fluctuations. This project aims to develop theoretical models for a new class of circuit-QED devices in which a JJ is embedded within a microwave cavity and a dc bias voltage applied rather than ac control fields, leading to the flow of a current of charges through the device. Such systems bring together two important subfields of physics: the quantum transport of charge (i.e. Cooper pairs) and the quantum optics of photons in the microwave cavity. Furthermore, the interactions between charges and photons are highly nonlinear and can be made exceptionally strong. The project will explore the fascinating physics of such systems and their connections with other driven-dissipative quantum systems.