Recovering articulated shape and motion, especially human body motion, from video is a challenging problem with a wide range of applications in medical study, sport analysis, animation, and so forth. Previous work on articulated motion recovery generally requires prior knowledge of the kinematic chain and usually does not concern the recovery of the articulated shape. The nonrigidity of some articulated part, for example, human body motion with nonrigid facial motion, is completely ignored. We propose a factorization-based approach to recover the shape, motion, and kinematic chain of an articulated object with nonrigid parts altogether directly from video sequences under a unified framework. The proposed approach is based on our modeling of the articulated nonrigid motion as a set of intersecting motion subspaces. A motion subspace is the linear subspace of the trajectories of an object. It can model a rigid or nonrigid motion. The intersection of two motion subspaces of linked parts models the motion of an articulated joint or axis. Our approach consists of algorithms for motion segmentation, kinematic chain building, and shape recovery. It handles outliers and can be automated. We test our approach through synthetic and real experiments and demonstrate how to recover an articulated structure with nonrigid parts via a single-view camera without prior knowledge of its kinematic chain.