Evolutionary processes leave footprints across the genome over time. Highly homozygous 11 regions may correspond to positive selection of favourable alleles, while maintenance of 12 heterozygous regions may be due to balancing selection phenomena. We analyzed 176 genomes 13 coming from 20 sequenced US fish and 156 fish from three different French lines that were 4 genotyped using a HD Axiom Trout Genotyping 665K SNP Array. Using methods based on 15 either Run of Homozygosity or Extended Haplotype Homozygosity, we detected selection 16 signals in four domesticated rainbow trout populations. Nine genomic regions composed of 253 17 genes, mainly located on chromosome 2 but also on chromosomes 12, 15, 16, and 20, were 18 identified under positive selection in all four populations. In addition, four heterozygous regions 19 containing 29 genes putatively under balancing selection were also shared by the four 20 populations and located on chromosomes 10, 13, and 19. Whatever the homozygous or 21 heterozygous nature of the region, we always found some genes highly conserved among 22 vertebrates due to their critical roles in cellular and nuclear organisation, embryonic 23 development or immunity. We identify new promising candidate genes involved in rainbow trout fitness, as well as genes already detected under positive selection in other fishes (auts2, 25 atp1b3, zp4, znf135, igf-1α, brd2, col9a2, mrap2, pbx1, emilin-3). These findings represent a 26 genome-wide map of signatures of selection common over rainbow trout populations, which is 27 the foundation to understand the processes in action and to identify what kind of diversity 28 should be preserved, or conversely avoided in breeding programs, in order to maintain or 29 improve essential biological functions in domesticated rainbow trout populations.