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Bundle adjustment jointly optimizes camera intrinsics and extrinsics and 3D point triangulation to reconstruct a static scene. The triangulation constraint, however, is invalid for moving points captured in multiple unsynchronized videos and bundle adjustment is not designed to estimate the temporal alignment between cameras. We present a spatiotemporal bundle adjustment framework that jointly optimizes four coupled sub-problems: estimating camera intrinsics and extrinsics, triangulating static 3D points, as well as sub-frame temporal alignment between cameras and computing 3D trajectories of dynamic points. Key to our joint optimization is the careful integration of physics-based motion priors within the reconstruction pipeline, validated on a large motion capture corpus of human subjects. We devise an incremental reconstruction and alignment algorithm to strictly enforce the motion prior during the spatiotemporal bundle adjustment. This algorithm is further made more efficient by a divide and conquer scheme while still maintaining high accuracy. We apply this algorithm to reconstruct 3D motion trajectories of human bodies in dynamic events captured by multiple uncalibrated and unsynchronized video cameras in the wild. To make the reconstruction visually more interpretable, we fit a statistical 3D human body model to the asynchronous video streams.Compared to the baseline, the fitting significantly benefits from the proposed spatiotemporal bundle adjustment procedure. Because the videos are aligned with sub-frame precision, we reconstruct 3D motion at much higher temporal resolution than the input videos.