Blur in photos due to camera shake, blur in astronomical image sequences due to atmospheric turbulence, and blur in magnetic resonance imaging sequences due to object motion are examples of blur that can not be adequately described as a space-invariant convolution, because such blur varies across the image. In this talk, we present a class of linear transformations, that are expressive enough for space-variant blurs, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on the above-mentioned examples demonstrate the practical significance of our approach.