International audience; • Only a few studies assess the impacts of local REDD+ initiatives on forests, due to the financial, methodological, data and political challenges of implementing rigorous impact evaluations.• Local REDD+ projects and programmes frequently include a mix of interventions, i.e., incentives, disincentives and enabling measures. Disincentives are used to reduce deforestation, and incentives – either conditional on results or not – are used to help minimise the trade-offs between carbon and well-being outcomes. • The scarce evidence that is available on local REDD+ outcomes shows modestly encouraging results for forest conservation and carbon stock enhancement. Three projects using conditional incentives showed positive results for forests, through reducing the negative impacts of smallholder agriculture and firewood collection.