Delivering the Sustainable Development Goals (SDGs) requires balancing demands on land between agriculture (SDG 2) and biodiversity (SDG 15). The rapidly increasing production of vegetable oils in general, and palm oil in particular, is perhaps the most controversial illustration of these trade-offs. We review palm oil production in the context of global vegetable oil crops and identify a wide range of negative environmental and biodiversity impacts. Oil palm, however, generally produces more oil per area than other crops, is economically viable in sites unsuitable for most other crops, and offers otherwise scarce economic opportunities to many rural people. Consideration of the relative yields, land requirements, and environmental impacts of different oil crops is crucial to guide decision-making. Reducing palm oil production while the demand for vegetable oil is growing would disproportionately increase global land needs for oil production, impacting food security, climate change, land degradation and other concerns.