Negative emissions technologies (NETs) are an essential part of most scenarios for achieving the Paris Agreement goal of limiting warming to below 2°C and for all scenarios that limit warming to 1.5 °C. The deployment of these technologies requires carbon accounting methods for a range of different purposes, such as determining the effectiveness of specific technologies or incentivising NETs. Although the need for carbon accounting methods is discussed within the literature on NETs, there does not appear to be a clear understanding of the range of different accounting challenges. Based on a systematic literature review this study identifies five distinct accounting issues related to NETs: 1. estimating total system-wide change in emissions/removals; 2. non-permanence; 3. nonequivalence of 'no overshoot' and 'overshoot and removal'; 4. accounting for incentives for NETs; and 5. the temporal distribution of emissions/removals. Solutions to these accounting challenges are proposed, or alternatively, areas for further research and the development of solutions are highlighted. One key recommendation is that carbon accounting methods should follow a 'reality principle' to report emissions and removals when and where they actually occur, and an important overall conclusion is that it is essential to use the correct accounting method for its appropriate purpose. For example, consequential methods that take account of total system-wide changes in emissions/removals should be used if the purpose is to inform decisions on the deployment or incentivisation of NETs. Attributional methods, however, should be used if the purpose is to construct static descriptions of possible net zero worlds.