The problem of multi-target tracking is comprised of two distinct, but tightly coupled challenges: (i) the naturally discrete problem of data association, \ie assigning image observations to the appropriate target; (ii) the naturally continuous problem of trajectory estimation, \ie recovering the trajectories of all targets. To go beyond simple greedy solutions for data association, recent approaches often perform multi-target tracking using discrete optimization. This has the disadvantage that trajectories need to be pre-computed or represented discretely, thus limiting accuracy. In this paper we instead formulate multi-target tracking as a discrete-continuous problem that handles each aspect in its natural domain and allows one to leverage powerful algorithms for multi-model fitting. Data association is performed using discrete optimization with label costs, and can be solved to near optimality. Trajectory estimation is posed as a continuous fitting problem with a simple closed-form solution, which is used in turn to update the label costs. We demonstrate the accuracy and robustness of our approach with state-of-the-art performance on several standard datasets.