The domain of spatiotemporal applications is a treasure trove of new types of data and queries. In this work, the focus is on a spatiotemporal sub-domain, namely the trajectories of moving point objects. We examine the issues posed by this type of data with respect to indexing and point out existing approaches and research directions. An important aspect of movement is the scenario in which it occurs. Three different scenarios, namely unconstrained movement, constrained movement, and movement in networks are used to categorize various indexing approaches. Each of these scenarios give us different means to either simplify indexing, or to improve the overall query processing performance.