Traditional worst-case analysis of geometric algorithms often fails to predict their performance in practice, because the worst-case running time only arises for very contrived inputs. As a result, practically efficient algorithms are sometimes discarded because their worst-case performance is bad. This has lead to research into the design and analysis of geometric algorithms for so-called realistic input models, in particular algorithms for fat objects and low density scenes. In this talk I will survey some of the results that have been obtained in this area.