We consider the problem of reconstructing a dynamic scene observed from a stereo camera. Most existing methods for depth from stereo treat different stereo frames independently, leading to temporally inconsistent depth predictions. Temporal consistency is especially important for immersive AR or VR scenarios, where flickering greatly diminishes the user experience. We propose DynamicStereo, a novel transformer-based architecture to estimate disparity for stereo videos. The network learns to pool information from neighboring frames to improve the temporal consistency of its predictions. Our architecture is designed to process stereo videos efficiently through divided attention layers. We also introduce Dynamic Replica, a new benchmark dataset containing synthetic videos of people and animals in scanned environments, which provides complementary training and evaluation data for dynamic stereo closer to real applications than existing datasets. Training with this dataset further improves the quality of predictions of our proposed DynamicStereo as well as prior methods. Finally, it acts as a benchmark for consistent stereo methods.