The paper presents a self-contained overview of various reduction techniques for symplectic and Poisson manifolds possessing symmetries. First, the standard Marsden-Weinstein symplectic reduction is presented. Then the optimal momentum map (a notion due to the authors) is introduced and its relation to generalized distributions is explained. The optimal momentum map is interpreted as the momentum map of a certain groupoid action. The paper proceeds to describe some generalizations of the classical Marsden-Weinstein reduction to some singular cases. At the end, the main theorems of Poisson reduction as well as an extension of the reduction techniques to certain non-Poisson submanifolds are described. Most ot the theorems are presented without proofs. A lot of examples are given throughout the paper.