Aim High levels of species richness in mountains are associated with their hypothetical roles as cradles and/or museums of diversity, but the generality of these roles remains unknown. To fill this gap, we tested these two hypotheses at a global scale and assessed the direct and indirect effects of abiotic regional features on the variation of montane amphibian richness world-wide. Location Global. Time period The last c. 300 Myr. Major taxa studied Amphibians. Methods Using an amphibian phylogeny containing 7,238 species, along with species distribution and climatic data, we estimated species richness, speciation rates, evolutionary time, terrain roughness, area and climatic stability for 514 mountain ranges. We evaluated the direct and indirect effects of these variables on richness patterns across these mountains using structural equation models. Results We found that most diverse mountain ranges for amphibians are concentrated in the Neotropics, but the fastest speciation rates are not restricted to this region. Instead, we found that evolutionary time, area and climatic stability better explained the global patterns of amphibian diversity in mountains. Species richness is higher in mountain regions with large and climatically stable areas, where early-derived lineages originated/established and accumulated through time. Main conclusions Mountains host an invaluable biodiversity shaped through deep time. Differences in speciation rates do not play a major role in explaining amphibian species richness across mountains. Instead, mountains experiencing milder historical climatic oscillations and having greater available areas for species persistence are likely to have faced lower extinction rates, leading to an increased accumulation of amphibian species through time. This condition highlights the importance of mountains as museums of deep evolutionary legacies and species-rich biotas.