Simultaneous localization and mapping (SLAM) is the process by which a robot constructs a global model of an environment from local observations of it; this is a fundamental perceptual capability supporting planning, navigation, and control. We are interested in improving the expressiveness and operational longevity of SLAM systems. In particular, we are interested in leveraging state-of-the-art machine learning methods for object detection to augment the maps robots can build with object-level semantic information. To do so, a robot must combine continuous geometric information about its trajectory and object locations with discrete semantic information about object classes. This problem is complicated by the fact that object detection techniques are often unreliable in novel environments, introducing outliers and making it difficult to determine the correspondence between detected objects and mapped landmarks. For robust long-term navigation, a robot must contend with these discrete sources of ambiguity. Finally, even when measurements are not corrupted by outliers, long-term SLAM remains a challenging computational problem: typical solution methods rely on local optimization techniques that require a good “initial guess,” and whose computational expense grows as measurements accumulate. The first contribution of this thesis addresses the problem of inference for hybrid probabilistic models, i.e., models containing both discrete and continuous states we would like to estimate. These problems frequently arise when modeling e.g., outlier contamination (where binary variables indicate whether a measurement is corrupted), or when performing object-level mapping (where discrete variables may represent measurement-landmark correspondence or object categories). The former application is crucial for designing more robust perception systems. The latter application is especially important for enabling robots to construct semantic maps; that is, maps containing objects whose states are a mixture of continuous (geometric) information and (discrete) categorical information (such as class labels). The second contribution of this thesis is, a novel spectral initialization method which is efficient to compute, easy to implement, and admits the first formal performance guarantees for a SLAM initialization method. The final contribution of this thesis aims to curtail the growing computational expense of long-term SLAM. In particular, we propose an efficient algorithm for graph sparsification capable of reducing the computational burden of SLAM methods without significantly degrading SLAM solution quality. Taken together, these contributions improve the robustness and efficiency of robot perception approaches in the lifelong setting.