Algebraic geometry and combinatorics play an important role in the analysis of phylogenetic models. I will give a brief overview of toric geometry. Then I will introduce a particular phylogenetic model, called the Cavander-Farris-Neyman model with a molecular clock, and I will discuss how we can study this model from the point of view of toric geometry and polytopes. I will present results about the vertex description, facet description and volume of the associated polytope, and about Grobner bases for the toric ideal of the model.