Understanding long‐term changes in ecological communities during global change is a priority for 21st‐century ecology. Deserts, already at climatic extremes, are of unique interest because they are projected to be ecosystems most responsive to global change. Within a 500‐km2 landscape in the Mojave Desert, USA, we measured perennial plant communities at 100 sites three times (1979, 2008, and 2016) during 37 yr to evaluate six hypotheses of community change. These hypotheses encompassed shifts in community measures (e.g., diversity, cover) and species elevational distributions, biotic homogenization, disproportionately large change at the highest elevations, relationships between turnover and species’ responses to disturbance and drought, and that environmental refugia (e.g., moist topographic positions) would receive species during climatic warming and drying. Most community measures changed temporally, such as species density (species/600 m2) increasing 23% and plant cover doubling between 1979 and 2016. There was no increase in nonnative species and minimal evidence for biotic homogenization. High‐elevation communities did not display greater change than low‐elevation communities. Moreover, environmental refugia factored little in species shifts. While species distributional changes were unrelated to affinity for disturbance, the six most persistent species (persisting on >80% of sites) were long‐lived shrubs not associated with disturbance. Overall, seemingly paradoxically, climatic warming and drying was associated with increasing plant abundance. Comparing the 1970s to 2007–2016, precipitation in the study area declined 16% from 17 to 14 cm/yr and average daily minimum temperature rose 13% (1.2°C). The current climate with fewer freezes, together with reduced grazing, could be among the most optimal for desert perennials in the past century, although potential response lags to continuing warming and drying are uncertain. This study of long‐term elevational shifts in communities during global change is among few in deserts, and the average upward elevational shift of 6 m/decade for species in our study is within the range reported for temperate biomes. However, the 41% of species moving downslope is unusually high. We propose that dynamics within desert perennial communities follow a core‐transient species model where a site's species are either highly persistent or transient in approximately equal proportions.