Hundreds of projects to reduce emissions from deforestation and forest degradation and enhance carbon stocks (REDD+) are implemented globally, many by non-governmental organizations (NGOs) or for-profit companies. Yet, at the global level, the Paris Agreement focuses on jurisdictional (national and subnational) REDD+. We ask: (1) How much can REDD+ projects contribute to achieving national and international climate objectives? (2) What are the issues in integrating REDD+ projects into national carbon accounting? Our snapshot of 377 REDD+ projects covering 53 million ha in 56 countries is based on data from the International Database on REDD+ Projects (ID-RECCO) supplemented with new data on projects' accounting methods. The number of new REDD+ projects declined steadily from 45 new projects in 2011 to five in 2019. We examined 161 certified projects that started between 2007 and 2017; 96 of these could sell carbon credits in voluntary carbon markets by 2020 and spent on average 4.7 (± 2.4) years between project start and sales in voluntary carbon markets. Globally, REDD+ projects claim to reduce an average of 3.67 tCO2e/ha annually. This figure - combined with projects limited coverage - implies that projects need to be upscaled more than 40x to fulfil the potential contribution of tropical and subtropical forests towards limiting global warming to well below 2oC. Compared to the national carbon accounting methods, most projects in Colombia, Indonesia and Peru (63 of 86) use at least one different carbon accounting parameter. Carbon accounting inconsistencies across levels need to be addressed. Overall, the argument for REDD+ projects lies in the emissions reductions they can achieve, diversifying participation in REDD+ and providing non-carbon benefits to local communities, potentially leading to broader support for climate action.