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Objection detection (OD) has been one of the most fundamental tasks in computer vision. Recent developments in deep learning have pushed the performance of image OD to new heights by learning-based, data-driven approaches. On the other hand, video OD remains less explored, mostly due to much more expensive data annotation needs. At the same time, multi-object tracking (MOT) which requires reasoning about track identities and spatio-temporal trajectories, shares similar spirits with video OD. However, most MOT datasets are class-specific (e.g., person-annotated only), which constrains a model's flexibility to perform tracking on other objects. We propose TrIVD (Tracking and Image-Video Detection), the first framework that unifies image OD, video OD, and MOT within one end-to-end model. To handle the discrepancies and semantic overlaps of category labels across datasets, TrIVD formulates detection/tracking as grounding and reasons about object categories via visual-text alignments. The unified formulation enables cross-dataset, multi-task training, and thus equips TrIVD with the ability to leverage frame-level features, video-level spatio-temporal relations, as well as track identity associations. With such joint training, we can now extend the knowledge from OD data, that comes with much richer object category annotations, to MOT and achieve zero-shot tracking capability. Experiments demonstrate that multi-task co-trained TrIVD outperforms single-task baselines across all image/video OD and MOT tasks. We further set the first baseline on the new task of zero-shot tracking.