The challenging task of multi-object tracking (MOT) requires simultaneous reasoning about track initialization, identity, and spatio-temporal trajectories. We formulate this task as a frame-to-frame set prediction problem and introduce TrackFormer, an end-to-end trainable MOT approach based on an encoder-decoder Transformer architecture. Our model achieves data association between frames via attention by evolving a set of track predictions through a video sequence. The Transformer decoder initializes new tracks from static object queries and autoregressively follows existing tracks in space and time with the conceptually new and identity preserving track queries. Both query types benefit from self- and encoder-decoder attention on global frame-level features, thereby omitting any additional graph optimization or modeling of motion and/or appearance. TrackFormer introduces a new tracking-by-attention paradigm and while simple in its design is able to achieve state-of-the-art performance on the task of multi-object tracking (MOT17) and segmentation (MOTS20). The code is available at https://github.com/timmeinhardt/TrackFormer