Phylogenetic trees are graph-like structures whose topology describes the inferred pattern of relationships among a set of biological entities, such as species or DNA sequences. Inference of these phylogenies typically involves evaluating large numbers of possible solutions and choosing the optimal topology, or set of topologies, from among all evaluated solutions. Such analyses are computationally intensive, especially when the pattern of relationships among a large number of entities is being sought. This thesis introduces two novel algorithms for the inference of large trees; one is applicable to the likelihood framework, the other to the Bayesian framework. Both approaches rely on the notion of a multi-modal tree 'landscape' through which inferential algorithms traverse. Using sampling techniques, the landscape can be perturbed sequentially, such that local optima can be evaded. The algorithms find good solutions in reasonable time, as demonstrated using real and simulated data sets. An example of large phylogeny inference is presented in the form of a novel estimate of Primate phylogeny- the largest estimate for this Order to date. The phylogeny is based on previously published smaller phylogenies, and hence serves as a summary of the present state of Primate phylogeny. In addition to this 'supertree's' topology, composite estimates of divergence are provided also. These estimates are based on multiple, clock-like genes combined using a novel approach presented here. Handling sets of trees and sequences poses practical problems in terms of conversion of data and the interoperation between computer programs. The thesis therefore concludes with a chapter discussing suitable data structures and programming patterns for phylogenetics. The appendix discusses an implementation of some of these concepts in an object-oriented application programming interface.