Distance methods, along with character methods and likelihood methods, form one of the three major approaches to estimating phylogenies from DNA or protein sequence data. Distance methods all start by estimating the evolutionary distances between pairs of extant species, and then seek to build phylogenies that fit the estimated distances as closely as possible. We survey the leading methods, including the popular neighbor-joining algorithm, various least-squares methods, and minimum evolution methods. We consider the algebraic basis common to these methods, and show how the slight differences in approaches lead to significant differences in computational time requirements. Finally, we consider how the various methods perform when tested against simulated data generated under biologically reasonable conditions.