Interpreting the functional content of a given genomic sequence is one of the central challenges of biology today. Perhaps the most promising approach to this problem is based on the comparative method of classic biology in the modern guise of sequence comparison. For instance, protein-coding regions tend to be conserved between species. Hence, a simple method for distinguishing a functional exon from the chance absence of stop codons is to investigate its homologue from closely related species. Predicting regulatory elements is even more difficult than exon prediction, but again, comparisons pinpointing conserved sequence motifs upstream of translation start sites are helping to unravel gene regulatory networks. In addition to interspecific studies, intraspecific sequence comparison yields insights into the evolutionary forces that have acted on a species in the past. Of particular interest here is the identification of selection events such as selective sweeps. Both intra- and interspecific sequence comparisons are based on a variety of computational methods, including alignment, phylogenetic reconstruction, and coalescent theory. This article surveys the biology and the central computational ideas applied in recent comparative genomics projects. We argue that the most fruitful method of understanding the functional content of genomes is to study them in the context of related genomic sequences. In particular, such a study may reveal selection, a fundamental pointer to biological relevance.