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Video transformers have recently emerged as an effective alternative to convolutional networks for action classification. However, most prior video transformers adopt either global space-time attention or hand-defined strategies to compare patches within and across frames. These fixed attention schemes not only have high computational cost but, by comparing patches at predetermined locations, they neglect the motion dynamics in the video. In this paper, we introduce the Deformable Video Transformer (DVT), which dynamically predicts a small subset of video patches to attend for each query location based on motion information, thus allowing the model to decide where to look in the video based on correspondences across frames. Crucially, these motion-based correspondences are obtained at zero-cost from information stored in the compressed format of the video. Our deformable attention mechanism is optimised directly with respect to classification performance, thus eliminating the need for suboptimal hand-design of attention strategies. Experiments on four large-scale video benchmarks (Kinetics-400, Something-Something-V2, EPIC-KITCHENS and Diving-48) demonstrate that, compared to existing video transformers, our model achieves higher accuracy at the same or lower computational cost, and it attains state-of-the-art results on these four datasets.