We introduce an approach for detecting and tracking detailed 3D poses of multiple people from a single monocular camera stream. Our system maintains temporally coherent predictions in crowded scenes filled with difficult poses and occlusions. Our model performs both strong per-frame detection and a learned pose update to track people from frame to frame. Rather than match detections across time, poses are updated directly from a new input image, which enables online tracking through occlusion. We train on numerous image and video datasets leveraging pseudo-labeled annotations to produce a model that matches state-of-the-art systems in 3D pose estimation accuracy while being faster and more accurate in tracking multiple people through time. Code and weights are provided at https://github.com/apple/ml-comotion