Many statistical problems arising in the context of multi-dimensional tables of non-negative counts (known as contingency tables) have natural representations in algebraic and polyhedral geometry. I will introduce some of these problems in the context of actual examples of large sparse tables and talk about how we have treated them and why. For example, our work on bounds for contingency table entries has been motivated by problems arising in the context of the protection of confidential statistical data results on decompositions related to graphical model representations have explicit algebraic geometry formulations. Similarly, results on the existence of maximum likelihood estimates for log-linear models are tied to polyhedral representations. It turns out that there are close linkages that I will describe.