Abstract. In this survey we compare the similarities, differences and the complexities of two very different approaches to solve a general constraint satisfaction probblems (CSP). One is the algorithm used in Moser’s ingenious proof of a constructive version of Lov´asz Local Lemma [3], the other is the k-SAT random walk algorithm from [5, 6], generalized to CSP’s. There are several similarities, both algorithms use a version of stochastic local search (SLS), but the kind of local search neighborhood is defined differently, also the preconditions for the algorithms to work (efficiently) are quite different.