Navigation, the task that comprises of determining collision-free motions for a robot from one configuration to another, has been predominantly researched from two angles: (i) Mapless methods and (ii) Map-based methods. This review will describe the work on (a) Bug algorithms and their derivatives which form the core of Mapless methods and (b) Voronoi graphs, visibility graphs and similar structures that form the core of Map-based methods. The review will also discuss aspects of probabilistic robotics, an emerging domain that examines navigation and other problems in the context of measurements provided by imperfect and noisy sensors. Finally, the review will touch upon emerging VLSI architectures for navigation and other tasks. © 2009 Nova Science Publishers, Inc.