This review highlights the major advantages and challenges of mechanically driven heat pumps and refrigeration systems with focus on multi-temperature applications. Different design strategies are presented, including cycles with multi-stage compressors, ejectors, expansion valves, cascades, and separated gas coolers. Most multi-temperature heat pump cycles use two heat sources and one heat sink. In supermarket applications, multi-stage compressor cycles with transcritical CO2 is an established key technology. Cascades with secondary loops are another frequently applied type of system. Expansion valve cycles are applied in household refrigeration and air conditioning. Cycles with ejectors seem to be a promising modification for system performance improvement. Separated gas coolers for space heating and hot water production have recently attracted attention due to the possible combination with supercritical CO2 cycles. Thermodynamic simulations reveal that multi-stage compressor cycles have the highest COPs and second law efficiencies, followed by cascade, ejector, and expansion valve cycles. The baseline cycle consisting of two single-stage heat pumps in parallel shows lower second law efficiency than the multi-stage compressor and cascade cycles, and higher efficiency than the ejector and expansion valve cycles. (C) 2016 Elsevier Ltd and IIR. All rights reserved.