Abstract: Phylogenetic trees are used in many ways in modern biology; for instance the tree of HIV strains is very important to the udnerstanding of drug resistant mutations. Making inferences about these trees is a hard mathematical, because, as I will show they do not lie in an ordinary Euclidean space. I will show how statistical inferential methods with trees needs computational topology to answer some of the questions currently asked by biologists. Will talk about the interface between statistics and computational algebraic geometry.