The paper summarises a global assessment of around 30 prospective negative emissions techniques (NETs) found in the literature. Fourteen techniques including direct air capture, BECCS, biochar, and ocean alkalinity enhancement are considered in more detail. The novel functional categorisation of NETs developed in the course of the assessment is set out and a comparative quantitative summary of the results is presented, focusing on the relative readiness, global capacity, costs and side-effects of the prospective NETs. Both technology specific and more generic potential limitations are discussed, notably those arising from energy requirements, from availability of geological storage capacity and from sustainable supply of biomass. Conclusions are drawn regarding the overall scope of NETs to contribute to safe carbon budgets, and challenges arising in the future governance of NETs, with particular reference to the potential role of carbon markets.