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The independence conditions of log-linear models in statistics are given by binomial equations, which means that methods from toric algebra and toric geometry are applicable to study such models. In this talk we examine undirected graphical models. This represents ongoing joint work with Dan Geiger (Microsoft) and Chris Meek (Technion). We characterize decomposable models via quadratic Gr"obner bases, and we propose an extension of the Hammersley-Clifford Theorem to non-decomposable models. There are numerous fascinating open problems in this field, and I will discuss several of them. For instance: what is the algebraic degree of the maximum likelihood estimator (inverse of the moment map) for a graphical model ? Two basic references for the statistical terms appearing in this talk are: S.L. Lauritzen: Graphical Models. The Clarendon Press, Oxford University Press, New York, 1996. R.C. Christensen: Log-Linear Models. Springer Texts in Statistics, Springer, New York, 1990