In this thesis, we present three main contributions to laser-based detection and tracking of dynamic objects, from both a model-based point of view and a model-free point of view, with an emphasis on applications to autonomous driving. A segmentation-based detector is first proposed to provide an end-to-end detection of the classes car, pedestrian and bicyclist in 3D laser data amongst significant background clutter. We postulate that, for the particular classes considered, solving a binary classification task outperforms approaches that tackle the multi-class problem directly. This is confirmed using custom and third-party datasets gathered of urban street scenes. The sliding window approach to object detection, while ubiquitous in the Computer Vision community, is largely neglected in laser-based object detectors, possibly due to its perceived computational inefficiency. We give a second thought to this opinion in this thesis, and demonstrate that, by fully exploiting the sparsity of the problem, exhaustive window searching in 3D can be made efficient. We prove the mathematical equivalence between sparse convolution and voting, and devise an efficient algorithm to compute exactly the detection scores at all window locations, processing a complete Velodyne scan containing 100K points in less than half a second. Its superior performance is demonstrated on the KITTI dataset, and compares commensurably with state of the art vision approaches. A new model-free approach to detection and tracking of moving objects with a 2D lidar is then proposed aiming at detecting dynamic objects of arbitrary shapes and classes. Objects are modelled by a set of rigidly attached sample points along their boundaries whose positions are initialised with and updated by raw laser measurements, allowing a flexible, nonparametric representation. Dealing with raw laser points poses a significant challenge to data association. We propose a hierarchical approach, and present a new variant of the well-known Joint Compatibility Branch and Bound algorithm to handle large numbers of measurements. The system is systematically calibrated on real world data containing 7.5K labelled object examples and validated on 6K test cases. Its performance is demonstrated over an existing industry standard targeted at the same problem domain as well as a classical approach to model-free tracking.