The molecular basis of convergent phenotypes is often unknown. However, convergence at a genomic level is predicted when there are large population sizes, gene flow among diverging lineages or strong genetic constraints. We used whole-genome resequencing to investigate genomic convergence in fishes ( Poecilia spp.) that have repeatedly colonized hydrogen sulfide (H2S)-rich environments in Mexico. We identified genomic similarities in both single nucleotide polymorphisms (SNPs) and structural variants (SVs) among independently derived sulfide spring populations, with approximately 1.2% of the genome being shared among sulfidic ecotypes. We compared these convergent genomic regions to candidate genes for H2S adaptation identified from transcriptomic analyses and found that a significant proportion of these candidate genes (8%) were also in regions where sulfidic individuals had similar SNPs, while only 1.7% were in regions where sulfidic individuals had similar SVs. Those candidate genes included genes involved in sulfide detoxification, the electron transport chain (the main toxicity target of H2S) and other processes putatively important for adaptation to sulfidic environments. Regional genomic similarity across independent populations exposed to the same source of selection is consistent with selection on standing variation or introgression of adaptive alleles across divergent lineages. However, combined with previous analyses, our data also support that adaptive changes in mitochondrially encoded subunits arose independently via selection on de novo mutations. Pressing questions remain on what conditions ultimately facilitate the independent rise of adaptive alleles at the same loci in separate populations, and thus, the degree to which evolution is repeatable or predictable. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.