Motion blur retains some information about motion, based on which motion may be recovered from blurred images. This is a difficult problem, as the situations of motion blur can be quite complicated, such as they may be space-variant, nonlinear, and local. This paper addresses a very challenging problem: can we recover motion blindly from a single motion-blurred image? A major contribution of this paper is a new finding of an elegant motion blur constraint. Exhibiting a very similar mathematical form as the optical flow constraint, this linear constraint applies locally to pixels in the image. Therefore, a number of challenging problems can be addressed, including estimating global affine motion blur, estimating global rotational motion blur, estimating and segmenting multiple motion blur, and estimating nonparametric motion blur field. Extensive experiments on blur estimation and image deblurring on both synthesized and real data demonstrate the accuracy and general applicability of the proposed approach.