The high global warming potential of current refrigerants in cooling equipment based on the vapor-compression cycle has triggered a major effort to find and implement more environmentally benign alternatives. Here, we review the basics of the vapor-compression cycle together with the safety, environmental, and thermodynamic constraints that have led to the current and next generation of refrigerants. The development of new fluids has focused on fluorinated olefins, known as hydrofluoroolefins (HFOs), and blends that contain HFOs. Many of these are slightly flammable, presenting trade-offs between safety and environmental considerations. Engineers also have options with a resurgence of the "natural refrigerants" (ammonia, carbon dioxide, propane, and isobutane). Innovative system designs that reduce the required quantity of refrigerant may allow a wider choice of refrigerants.