Abstract: In this talk I will address the link between solvable models of statistical mechanics and algebraic dynamical systems. The main reason to believe in the existence of a strong link is the remarkable coincidence of entropies of many celebrated solvable lattice models (dimer matchings, domino tilings, spanning trees, etc) and entropies of certain algebraic dynamical systems. Even though the question about the existence of such a link was raised almost two decades ago, this problem remained largely inaccessible. The development of the theory of symbolic covers of algebraic dynamical systems has only recently provided a suitable framework. I will describe in greater detail the link between the solvable sandpile models and their algebraic counterparts. The talk is based on a series of joint papers with D. Lind (Seattle) and K. Schmidt (Vienna).