We investigated spatial patterns of evolutionary relatedness and diversification rates to test hypotheses about the historical biogeographic processes underlying the radiation of Neotropical rats and mice (Sigmodontinae, ~400 species). A negative correlation between mean phylogenetic distance and diversification rates of rodent assemblages reveals a pattern of species co-occurrence in which assemblages of closely related species are also the fastest diversifying ones. Subregions of the Neotropics occupied by distantly related species that are on average more slowly diversifying include Central America, northern South America, and the Atlantic forest. In southern South America, recent species turnover appears to have been higher. Ancestral locations for the main tribes of sigmodontines were also estimated, suggesting eastern South America and the Amazonian lowlands were colonized before some central Andean regions, even though the latter are now centers of species richness for these rodents. Moreover, a past connection between the tropical Andes and the Atlantic Forest is suggested by our results, highlighting a role for a hypothetical arc connecting the two biomes, which would have impacted many other groups of organisms. Whether rapid, recent speciation in some regions is related to Quaternary climatic fluctuations and the young age of sigmodontines (~12.7 Ma crown age) or instead to intrinsic traits of these rodents remains an open question. If the former is true, we hypothesize that contrasting trends will characterize older Neotropical clades.