The task of tracking multiple targets is often addressed with the so-called tracking-by-detection paradigm, where the first step is to obtain a set of target hypotheses for each frame independently. Tracking can then be regarded as solving two separate, but tightly coupled problems. The first is to carry out data association, i.e., to determine the origin of each of the available observations. The second problem is to reconstruct the actual trajectories that describe the spatio-temporal motion pattern of each individual target. The former is inherently a discrete problem, while the latter should intuitively be modeled in continuous space. Having to deal with an unknown number of targets, complex dependencies, and physical constraints, both are challenging tasks on their own and thus most previous work focuses on one of these subproblems. Here, we present a multi-target tracking approach that explicitly models both tasks as minimization of a unified discrete-continuous energy function. Trajectory properties are captured through global label costs, a recent concept from multi-model fitting, which we introduce to tracking. Specifically, label costs describe physical properties of individual tracks, e.g., linear and angular dynamics, or entry and exit points. We further introduce pairwise label costs to describe mutual interactions between targets in order to avoid collisions. By choosing appropriate forms for the individual energy components, powerful discrete optimization techniques can be leveraged to address data association, while the shapes of individual trajectories are updated by gradient-based continuous energy minimization. The proposed method achieves state-of-the-art results on diverse benchmark sequences.