Deep borehole heat exchangers (DBHEs) with depths exceeding 500 m have been researched comprehensively in the literature, focusing on both applications and subsurface modelling. This review focuses on conventional (vertical) DBHEs and provides a critical literature survey to analyse (i) methodologies for modelling; (ii) results from heat extraction modelling; (iii) results from modelling deep borehole thermal energy storage; (iv) results from heating and cooling models; and (v) real case studies. Numerical models generally compare well to analytical models whilst maintaining more flexibility, but often with increased computational resources. Whilst in-situ geological parameters cannot be readily modified without resorting to well stimulation techniques (e.g. hydraulic or chemical stimulation), engineering system parameters (such as mass flow rate of the heat transfer fluid) can be optimised to increase thermal yield and overall system performance, and minimise pressure drops. In this active research area, gaps remain, such as limited detailed studies into the effects of geological heterogeneity on heat extraction. Other less studied areas include: DBHE arrays, boundary conditions and modes of operation. A small number of studies have been conducted to investigate the potential for deep borehole thermal energy storage (BTES) and an overview of storage efficiency metrics is provided herein to bring consistency to the reporting of thermal energy storage performance of such systems. The modifications required to accommodate cooling loads are also presented. Finally, the active field of DBHE research is generating a growing number of case studies, particularly in areas with low-cost drilling supply chains or abandoned hydrocarbon or geothermal wells suitable for repurposing. Existing and planned projects are thus presented for conventional (vertical) DBHEs. Despite growing interest in this area of research, further work is needed to explore DBHE systems for cooling and thermal energy storage.