Simultaneous localization and mapping (SLAM) is the process of constructing a global model from local observations, acquired as a mobile robot moves through an environment. SLAM is a foundational capability for mobile robots, supporting such core functions as planning, navigation, and control, for a wide range of application domains. SLAM is one of the most deeply investigated fields in mobile robotics research, yet many open questions remain to enable the realization of robust, long-term autonomy. This talk will review the historical development of SLAM and will describe several current research projects in our group. Two key themes are increasing the expressive capacity of the environmental models used in SLAM systems (representation) and improving the performance of the algorithms used to estimate these models from data (inference). Our ultimate goal is to provide autonomous robots with a more comprehensive understanding of the world, facilitating life-long learning in complex dynamic environments.