Overlapping genes are defined as a pair of protein-coding genes whose coding regions overlap on either the same strand or on the opposite strand. The sequence interdependence between two overlapping coding regions adds complexity to almost all molecular evolution analyses. Here, I use a comparative-genomic approach aimed at resolving several open questions concerning the evolution of overlapping genes. I demonstrate that estimates of selection intensity that ignore gene overlap are biased and that the magnitude and the direction of this bias is dependant on the type of overlap. I present a new method for the simultaneous estimation of selection intensities in overlapping genes. I show that overlapping genes are mostly subjected to purifying selection, in contradistinction to previous studies, which ignored the interdependence between overlapping reading frames and detected an inordinate prevalence of positive selection. Using simulation and two case studies, I show that this method can be used to distinguish between spurious and functional overlapping genes by using purifying selection as a tell-tale sign of functionality. In the first study, I test for the functionality of a hypothetical overlapping gene, which is central in the "Rosetta stone" hypothesis for the origin of the two aminoacyl tRNA synthetase classes from a pair of overlapping genes. I found no evidence of selection acting on the hypothetical gene, implying that the gene is non-functional, thus rejecting the "Rosetta stone" hypothesis. In the second study, I search for unannotated overlapping genes in viral genomes. I present evidence for the existence of a novel overlapping gene in the genomes of four viruses that infect Hymenoptera. In another study, I present a method for the detection of selection signatures on hypothetical overlapping genes using population-level data. I apply the method to test whether the hypothetical gene in influenza A is under selection. Finally, I study a previously unexplained difference in the frequencies of overlapping genes of different types. I show that the structure of the genetic code and the abundance of different amino acids in proteins explain this difference between overlap types and lead to a correlation between overlap frequency and genomic composition.