Our research programme in theoretical astrophysics studies the key physical processes which govern the evolution of the Universe. These can be broadly described as "accretion processes" and "dynamics", but these broad themes have applications across a very wide range of physical systems, from exoplanets, to super-massive black holes, to galaxies. Accretion of gas on to compact objects plays a critical role in the formation of stars, planets, and black holes, and accretion on to black holes is the most efficient way of extracting energy from conventional matter. At the same time, gravity's cumulative nature gives it a decisive role in determining the structure and evolution of matter at all scales. The theoretical understanding of these twin aspects - accretion, and the structure and evolution of the parent systems - are the key themes of our research, in various cosmic contexts. The complex nature of these processes means that much of our work involves large-scale numerical simulations, and as a result the School is host to one node of the UK's DiRAC high-performance computing facility. Our current research in theoretical astrophysics can be broken down into three broad areas, outlined below.