State-of-the-art multi-object tracking (MOT) methods follow the tracking-by-detection paradigm, where object trajectories are obtained by associating per-frame outputs of object detectors. In crowded scenes, however, detectors often fail to obtain accurate detections due to heavy occlusions and high crowd density. In this paper, we propose a new MOT paradigm, tracking-by-counting, tailored for crowded scenes. Using crowd density maps, we jointly model detection, counting, and tracking of multiple targets as a network flow program, which simultaneously finds the global optimal detections and trajectories of multiple targets over the whole video. This is in contrast to prior MOT methods that either ignore the crowd density and thus are prone to errors in crowded scenes, or rely on a suboptimal two-step process using heuristic density-aware point-tracks for matching targets. Our approach yields promising results on public benchmarks of various domains including people tracking, cell tracking, and fish tracking.