Extreme environments offer powerful opportunities to study how different organisms have adapted to similar selection pressures at the molecular level. Arctic plants have adapted to some of the coldest and driest biomes on Earth and typically possess suites of similar morphological and physiological adaptations to extremes in light and temperature. Here, we compare patterns of molecular evolution in three Brassicaceae species that have independently colonized the Arctic and present some of the first genetic evidence for plant adaptations to the Arctic environment. By testing for positive selection and identifying convergent substitutions in orthologous gene alignments for a total of 15 Brassicaceae species, we find that positive selection has been acting on different genes, but similar functional pathways in the three Arctic lineages. The positively selected gene sets identified in the three Arctic species showed convergent functional profiles associated with extreme abiotic stress characteristic of the Arctic. However, there was little evidence for independently fixed mutations at the same sites and for positive selection acting on the same genes. The three species appear to have evolved similar suites of adaptations by modifying different components in similar stress response pathways, implying that there could be many genetic trajectories for adaptation to the Arctic environment. By identifying candidate genes and functional pathways potentially involved in Arctic adaptation, our results provide a framework for future studies aimed at testing for the existence of a functional syndrome of Arctic adaptation in the Brassicaceae and perhaps flowering plants in general.