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The purpose of this Special Issue is to present new directions and new advances in limit theorems in probability theory. The list of topics can be very extensive, and it includes classical models of sums of both independent and various kinds of dependent random variables, limit theorems for random processes, functional limit theorems, limit theorems in high-dimensional spaces, limit theorems in free probability, probabilities of large deviations, small and large ball probabilities, measure concentration, and more.