Traditional approaches to simultaneous localization and mapping (SLAM) rely on low-level geometric features such as points, lines, and planes. They are unable to assign semantic labels to landmarks observed in the environment. Recent advances in object recognition and semantic scene understanding, however, have made this information easier to extract than ever before, and the recent proliferation of robots in human environments demand access to reliable semantic-level mapping and localization algorithms to enable true autonomy. Furthermore, loop closure recognition based on low-level features is often viewpoint dependent and subject to failure in ambiguous or repetitive environments, whereas object recognition methods can infer landmark classes and scales, resulting in a small set of easily recognizable landmarks. In this thesis, we present two solutions that incorporate semantic information into a full localization and mapping pipeline. In the first, we propose a solution method using only single-image bounding box object detections as the semantic measurement. As these bounding box measurements are relatively imprecise when projected back into 3D space and difficult to associate with existing mapped objects, we first present a general method to probabilistically compute data associations within an estimation framework and demonstrate its improved accuracy in the case of high-uncertainty measurements. We then extend this to the specific case of semantic bounding box measurements and demonstrate its accuracy in indoor and outdoor environments. Second, we propose a solution based on the detection of semantic keypoints. These semantic keypoints are not only more reliably positioned in space, but also allow us to estimate the full six degree-of-freedom pose of each mapped object. The usage of these semantic keypoints allows us to effectively reduce the problem of semantic mapping to that of the much more well studied problem of mapping point features, allowing for its efficient solution and robustness in practice. Finally, we present a method of robotic navigation in unexplored semantic environments that robustly plans paths through unknown and unexplored semantic environments towards a goal location. Through the use of the semantic keypoint-based semantic SLAM algorithm, we demonstrate the successful execution of navigation missions through on-the-fly generated semantic maps.