Lacking experimental data, protein function is often predicted from evolutionary and protein structure theory. Under the 'domain grammar' hypothesis the function of a protein follows from the domains it encodes. Under the 'orthology conjecture', orthologs, related through species formation, are expected to be more functionally similar than paralogs, which are homologs in the same or different species descended from a gene duplication event. However, these assumptions have not thus far been systematically evaluated. To test the 'domain grammar' hypothesis, we built models for predicting function from the domain combinations present in a protein, and demonstrated that multi-domain combinations imply functions that the individual domains do not. We also developed a novel gene-tree based method for reconstructing the evolutionary histories of domain architectures, to search for cases of architectures that have arisen multiple times in parallel, and found this to be more common than previously reported. To test the 'orthology conjecture', we first benchmarked methods for homology inference under the obfuscating influence of low-complexity regions, in order to improve the InParanoid orthology inference algorithm. InParanoid was then used to test the relative conservation of functionally relevant properties between orthologs and paralogs at various evolutionary distances, including intron positions, domain architectures, and Gene Ontology functional annotations. We found an increased conservation of domain architectures in orthologs relative to paralogs, in support of the 'orthology conjecture' and the 'domain grammar' hypotheses acting in tandem. However, equivalent analysis of Gene Ontology functional conservation yielded spurious results, which may be an artifact of species-specific annotation biases in functional annotation databases. I discuss possible ways of circumventing this bias so the 'orthology conjecture' can be tested more conclusively. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 6: Epub ahead of print.