Modern approaches for multi-person pose estimation in video require large amounts of dense annotations. However, labeling every frame in a video is costly and labor intensive. To reduce the need for dense annotations, we propose a PoseWarper network that leverages training videos with sparse annotations (every k frames) to learn to perform dense temporal pose propagation and estimation. Given a pair of video frames---a labeled Frame A and an unlabeled Frame B---we train our model to predict human pose in Frame A using the features from Frame B by means of deformable convolutions to implicitly learn the pose warping between A and B. We demonstrate that we can leverage our trained PoseWarper for several applications. First, at inference time we can reverse the application direction of our network in order to propagate pose information from manually annotated frames to unlabeled frames. This makes it possible to generate pose annotations for the entire video given only a few manually-labeled frames. Compared to modern label propagation methods based on optical flow, our warping mechanism is much more compact (6M vs 39M parameters), and also more accurate (88.7% mAP vs 83.8% mAP). We also show that we can improve the accuracy of a pose estimator by training it on an augmented dataset obtained by adding our propagated poses to the original manual labels. Lastly, we can use our PoseWarper to aggregate temporal pose information from neighboring frames during inference. This allows our system to achieve state-of-the-art pose detection results on the PoseTrack2017 and PoseTrack2018 datasets. Code has been made available at: https://github.com/facebookresearch/PoseWarper.