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Having been referred to as the Holy Grail of autonomous robotics research, simultaneous localization and mapping (SLAM) lies at the core of most the autonomous robotic applications. This article explains the recent advances in the representations of robotic sensor measurements and the map itself as well as their consequences on the robustness of SLAM. Fundamentally, the concept of a set-based measurement and map state representation allows all of the measurement information, spatial and detection, to be incorporated into joint Bayesian SLAM frameworks. Modeling measurements and the map state as random finite sets (RFSs) rather than the traditionally adopted random vectors is not merely a triviality of notation. It will be demonstrated that a set-based framework circumvents the necessity for any fragile data association and map management heuristics, which are necessary in vector-based solutions.