The rapidly increasing amount of available genomic sequence data provides an abundance of potential information for phylogenetic analyses. Many models and methods have been developed to build evolutionary trees based on this information. A common feature of most of these models is that they start out with fragments of the genome, called genes. Depending on the genes and species, and the methods used to perform the phylogenetic analyses, one typically ends up with a large number of phylogenetic trees which may not agree with one another. Simply put, the problem now is the following: Given several discordant phylogenetic trees as input, infer the (presumably) correct phylogeny. This thesis seeks to address some of the methodological and algorithmic challenges posed by this problem. In particular, we present two new algorithms related to inferring phylogenetic trees in the presence of gene duplication, and introduce a new distance measure for comparing phylogenetic trees.