Mobile computing emerged as a new application area due to recent advances in communication and positioning technology. As David Lomet (2002) notices, a substantial part of the conducted work refers to keeping track of the position of moving objects (automobiles, people, etc.) at any point in time. This information is very critical for decision making, and, since objects’ locations may change with relatively high frequency, this calls for providing fast access to object location information, thus rendering the indexing of moving objects a very interesting as well as crucial part of the area. In this chapter we present an overview on advances made in databases during the last few years in the area of mobile object indexing, and discuss issues that remain open or, probably, are interesting for related applications.