The experimental technique of angle-and spin-resolved ultraviolet photoemission has been developed into an important tool for investigating the electronic structure of crystalline materials. Together with the high level in experimental set-up tremendous progress has been achieved in the theoretical description of the photoemission process from solid surfaces. Due to the intensive combination of experimental and theoretical investigations, which has existed for more than 15 years in this area of physical interest, the understanding of the electronic properties of clean and adsorbate-covered surfaces and thin films has grown enormously. This paper reviews the theoretical developments in the field of ultraviolet photoemission. Starting with a brief overview about many-body description of photoemission theory, one-electron models will be introduced with special emphasis on applications. In particular, theoretical aspects like temperature-dependent effects due to phonon excitations, relativistic effects and the influence of strong electron correlations will be discussed, and their importance for quantitative photoemission calculations will be shown by several examples. Furthermore, the review inhibits the modern technique of fullpotential photoemission, which allows a more detailed understanding of complex systems like covalently bonded materials, multilayers and adsorbate-covered surfaces. Finally, the wide range of dichroic effects visible in photoemission experiments will be elucidated in the framework of relativistic photoemission theory.