Achieving global commitments on climate mitigation necessitates a rapid transition of the global energy system away from fossil fuels. Modelled scenarios within Integrated Assessment Models (IAMs) and Energy Systems Models (ESMs) indicate that limiting global temperature rise to safe levels will require some dependence on negative emissions technologies (NETs). However, the representation of NETs varies significantly across models, leading to differences in their roles across mitigation scenarios. Bioenergy with carbon capture and storage (BECCS) and direct air carbon capture and storage (DACCS) are two possible solutions that are directly related to the energy system. Here, we perform a systematic review of the representation of BECCS and DACCS within ESMs and IAMs, exploring their roles in decarbonisation scenarios and identifying how NETs contribute to energy system transition pathways.