Inaugural Lecture by Professor Steven Balbus looking at the history of the universe A one sentence summary of much of the history of our Universe might be that it is the formation of ever more complex and compact structure from a diffuse background. The build-up of a compact core of material from more tenuous surroundings is known as accretion, and it is a process common to much of astrophysics, from the early creation of giant clusters of galaxies to current star, planet, and black hole formation. In this Lecture, I will give a general and personal overview of accretion physics. I will discuss some of the theoretical successes the community has enjoyed in its struggle to understand accretion, together with ongoing challenges. Above all, I will try to convey a sense of the richness of accretion as a physical process, and the role it has played in enhancing a deeper understanding of many astrophysical phenomena. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/