The increasing amount of molecular data available for phylogenetic studies means that larger, often intra-species, data sets are being analysed. Treating such data sets with methods designed for small interspecies data may not be useful. This thesis comprises four projects within the field of phylogenetics that focus on cases where the application of current tree estimation methods is not sufficient to answer the biological questions of interest. A simulation study contrasts the accuracy of several tree estimation methods for a particular class of five-taxon, equal-rate, trees. This study highlights several difficulties with tree estimation, including the fact that some tree topologies produce “misleading" patterns that are incorrectly interpreted; that correction for multiple changes does not always increase accuracy, because of increased variance; and the difficulty of correctly placing outgroup taxa. A mitochondrial DNA data set, containing over 400 modern and ancient Adélie penguin samples, is used to estimate the rate of evolution. Straightforward tree-estimation is unhelpful because the amount of homoplasy in the data makes the construction of a single reliable tree impossible. Instead the data is represented by a network. A method, that extends statistical geometry, assesses whether or not a data set can be well-represented by a tree. The "tree-likeness" of each quartet in the data is evaluated and displayed visually, either for the entire data set or by taxon. This aids in identifying reticulate (or simply noisy) data sets, and also particular taxa that confound tree-like signal. Novel methods are developed that use pairwise dissimilarities between isolates in intra-species microbial data sets, to identify strains that are good representatives of their species or subspecies.