Cu/SSZ-13 SCR catalysts have been extensively studied in the past decade or so. Hydrothermal stability of these catalysts has been identified as the most important criterion for application. In this perspective, we describe recent atomic-level understanding of their hydrothermal stability. In particular, electron paramagnetic resonance (EPR) is shown to rather accurately quantify isolated Cu(II) ions and CuO clusters in fresh and aged catalysts to demonstrate the remarkable hydrothermal stability for Cu2+ ions located in 6-membered ring windows, and the conversion of [Cu(OH)](+) ions in Chabazite cages to CuO clusters. The hydrothermal stability difference of the two isolated Cu(II) ions is confirmed with DFT simulations and the conversion of [Cu(OH)](+) to CuO is proposed to involve formation, migration and condensation of Cu(OH)(2) intermediates. The structural destructive role of CuO clusters is attributed to mesopore formation from their migration, which more severely damages the catalysts than dealumination. Finally, perspectives are given on new strategies for low-temperature NOx removal, rational design and refinement of Cu/SSZ-13, and development of new Cu/zeolite SCR catalysts with even better performance than the state-of-the-art Cu/SSZ-13.