Given N real weights w1, w2, . . . , wN stored in one-dimensional array, we consider the problem for finding an optimal interval I [1, N] under certain criteria. We shall review efficient algorithms developed for solving such problems under several optimality criteria. This problem can be naturally extended to two-dimensional case. Namely, given a NN two-dimensional array of N2 reals, the problem seeks to find a subregion of the array (e. g. , rectangular subarray R) that optimizes a certain objective function. We shall also review several algorithms for such problems. We shall also mention applications of these problems to region segmentation in image processing and to data mining.