The last twenty or so years have witnessed a dramatic increase in the use of computational methods for inferring linguistic phylogenies. Although the results of this research have been controversial, the methods themselves are an undeniable boon for historical and Indo-European linguistics, if for no other reason than that they allow the field to pursue questions that were previously intractable. After a review of the advantages and disadvantages of computational phylogenetic methods, I introduce the following methods of phylogenetic inference in R: maximum parsimony; distance-based methods (UPGMA and neighbor joining); and maximum likelihood estimation. I discuss the strengths and weaknesses of each of these methods and in addition explicate various measures associated with phylogenetic estimation, including homoplasy indices and bootstrapping. Phylogenetic inference is carried out on the Indo-European dataset compiled by Don Ringe and Ann Taylor, which includes phonological, morphological, and lexical characters.