The rapidly growing scale of solar photovoltaics and wind energy coupled with electrification of transport, heating and industry offers an affordable pathway for achieving deep decarbonization. Massive integration of variable solar photovoltaics and wind energy requires large-scale adoption of short (seconds-hours) and long (hours-days) duration energy storage. Currently, long-duration pumped hydro energy storage (PHES) accounts for about 95% of global energy storage for the electricity sector. This paper discusses the Global PHES Atlases developed by the Australian National University which identify 0.8 million off-river (closed-loop) PHES sites with a combined 86 million Gigawatt-hours of storage potential, which is about 3 years of current global electricity production. These Atlases show that most global jurisdictions have vast potential for low-cost PHES with small water and land requirements, and that do not require new dams on rivers. The low capital cost of premium PHES systems ($ per kilowatt-hour) is pointed out. Methods for creating shortlists of promising PHES sites from the Atlases for detailed investigation are developed.