As a key component in many industrial heterogeneous catalysts, the surface structure and reactivity of ceria, CeO2, has attracted a lot of attention. In this topical review we discuss some of the approaches taken to form a deeper understanding of the surface physics and chemistry of this important and interesting material. In particular, we focus on the preparation of ultrathin ceria films, nanostructures and supported metal nanoparticles. Cutting-edge microscopic and spectroscopic experimental techniques are highlighted which can probe the behaviour of oxygen species and atomic defects on these model surfaces
