The paradigm of self-organized criticality was introduced about a decade ago by Bak, Tang, and Wiesenfeld. Good arguments can be given that the concept applies to a wide variety of systems far from equilibrium. Mathematical models, so-called sandpiles, can be viewed as discrete-time dynamical systems whose evolution contains simple random and simple deterministic elements. In principle, Markov matrices can be used to describe the statistical features of the evolution, but a complete analysis is out of reach. In the talk, I present results of direct numerical simulation, some limited analysis based on Markov matrices, and non--rigorous arguments of non--equilibrium statistical mechanics.