As whole-genome sequencing efforts extend beyond more traditional model organisms to include a deep diversity of species, comparative genomic analyses will be further empowered to reveal insights into the human genome and its evolution. The discovery and annotation of functional genomic elements is a necessary step toward a detailed understanding of our biology, and sequence comparisons have proven to be an integral tool for that task. This review is structured to broadly reflect the statistical challenges in discriminating these functional elements from the bulk of the genome that has evolved neutrally. Specifically, we review the comparative genomics literature in terms of specificity, sensitivity, and phylogenetic scope, as well as the trade-offs that relate these factors in standard analyses. We consider the impact of an expanding diversity of orthologous sequences on our ability to resolve functional elements. This impact is assessed through both recent comparative analyses of deep alignments and mathematical modeling.