This chapter discusses vapour compression-based heat pump (HP) systems and describes the thermodynamic cycle and its calculation, as well as the operating regimes of an HP with an electro-compressor. The energy, economic and environmental performance criteria, which show the opportunity to implement conventional HP and hybrid HP-PV systems in a heating/cooling system, are also presented. An additional energy performance indicator is considered, such as the global seasonal performance factor, which integrates the qualities of the HP and PV generator, as well as their interconnection, to assess the energy efficiency of the HP-PV hybrid system. The ineffectiveness of refrigerant can be used to quickly evaluate HP energy efficiency, provided the values of the operating temperatures and the Jacob number are known, which include the specific heat of the liquid refrigerant and the latent heat of condensation. Additionally, possible substitutes for non-ecological refrigerants used in HP equipment are identified, along with the primary evaluation indices in their selection process, such as total equivalent warming impact (TEWI). The types of HPs according to intermediate fluid–heat distribution fluid, including high-temperature HPs, air-source HPs (ASHPs), and ground-source HPs (GSHPs), are briefly described. A detailed theoretical study on GSHP technology, concentrating on ground-coupled HP (GCHP) systems, is also included. Then, a detailed description of GSHPs and their development is performed. The most typical simulation models and computer programs of the vertical ground heat exchangers (GHEs) in steady-state are currently available and summarised. A numerical simulation model of transient heat transfer in vertical GHEs in both double and single U-tube configurations is developed using the electrothermal analogy and solved with the finite difference method. Finally, some advanced engineering applications of hybrid GCHP systems and examples of HP utilisation are included.