Orthologues and paralogues are types of homologous genes that are related by speciation or duplication, respectively. Orthologous genes are generally assumed to retain equivalent functions in different organisms and to share other key properties. Several recent comparative genomic studies have focused on testing these expectations. Here we discuss the complexity of the evolution of gene-phenotype relationships and assess the validity of the key implications of orthology and paralogy relationships as general statistical trends and guiding principles.