We survey applications of classical and of time-sequential sampling theory and some of its recent extensions, respectively, in two complementary areas. First to reduce the computation for tomographic reconstruction from $O(N^3)$ to $O(N^2\log N)$ for an $N \times N$ image, with similar acceleration for 3D images. And second, to reduce acquisition requirements for dynamic imaging below those predicted by classical theory. In both areas, the savings demonstrated in practical examples exceed an order-of-magnitude.