The authors present a set of novel data structures for the efficient maintenance of various continuous and discrete attributes of mobile data. A Kinetic Data Structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. The authors develop a concentual framework for kinetic data structures, and propose a number of criteria for the quality of such structures. They describe a number of fundamental techniques for their design, and illustrate these general concepts by presenting kinetic data structures for maintaining the convex hull and the closest pair of moving points in the plane; these structures behave well according to the proposed quality criteria for KDSs. \(\copyright\) Academic Press.