We present a convolution-free approach to video classification built exclusively on self-attention over space and time. Our method, named "TimeSformer," adapts the standard Transformer architecture to video by enabling spatiotemporal feature learning directly from a sequence of frame-level patches. Our experimental study compares different self-attention schemes and suggests that "divided attention," where temporal attention and spatial attention are separately applied within each block, leads to the best video classification accuracy among the design choices considered. Despite the radically different design compared to the prominent paradigm of 3D convolutional architectures for video, TimeSformer achieves stateof-the-art results on several major action recognition benchmarks, including the best reported accuracy on Kinetics-400 and Kinetics-600. Furthermore, our model is faster to train and has higher test-time efficiency compared to competing architectures. Code and pretrained models will be made publicly available.