We present a robust and efficient approach to video stabilization that achieves high-quality camera motion for a wide range of videos. In this article, we focus on the problem of transforming a set of input 2D motion trajectories so that they are both smooth and resemble visually plausible views of the imaged scene; our key insight is that we can achieve this goal by enforcing subspace constraints on feature trajectories while smoothing them. Our approach assembles tracked features in the video into a trajectory matrix, factors it into two low-rank matrices, and performs filtering or curve fitting in a low-dimensional linear space. In order to process long videos, we propose a moving factorization that is both efficient and streamable. Our experiments confirm that our approach can efficiently provide stabilization results comparable with prior 3D methods in cases where those methods succeed, but also provides smooth camera motions in cases where such approaches often fail, such as videos that lack parallax. The presented approach offers the first method that both achieves high-quality video stabilization and is practical enough for consumer applications.