Orthologs and paralogs are two fundamentally different types of homologous genes that evolved, respectively, by vertical descent from a single ancestral gene and by duplication. Orthology and paralogy are key concepts of evolutionary genomics. A clear distinction between orthologs and paralogs is critical for the construction of a robust evolutionary classification of genes and reliable functional annotation of newly sequenced genomes. Genome comparisons show that orthologous relationships with genes from taxonomically distant species can be established for the majority of the genes from each sequenced genome. This review examines in depth the definitions and subtypes of orthologs and paralogs, outlines the principal methodological approaches employed for identification of orthology and paralogy, and considers evolutionary and functional implications of these concepts. Terms and Definitions Co-orthologs: two or more genes in one lineage that are, collectively, orthologous to one or more genes in another lineage due to a lineage-specific duplication(s) Homologs: genes sharing a common origin Inparalogs: paralogous genes resulting from a lineage-specific duplication(s) subsequent to a given speciation event Molecular clock: a central concept of molecular evolution, which posits that a gene evolves at a constant rate as long as its function does not change Orthologs: genes originating from a single ancestral gene in the last common ancestor of the compared genomes Outparalogs: paralogous genes resulting from a duplication(s) preceding a given speciation event Paralogs: genes related via duplication Pseudoorthologs: genes that actually are paralogs but appear to be orthologous due to differential, lineage-specific gene loss Pseudoparalogs: homologous genes that come out as paralogs in a single-genome analysis but actually ended up in the given genome as a result of a combination of vertical inheritance and HGT Xenologous gene displacement: displacement of a gene in a given lineage with a member of the same orthologous cluster from a distant lineage (xenolog)