Understanding the relationship between stand-level tree diversity and productivity has the potential to inform the science and management of forests. History shows that plant diversity-productivity relationships are challenging to interpret—and this remains true for the study of forests using non-experimental field data. Here we highlightpitfalls regarding the analyses and interpretation of such studies. We examine three themes:1) the nature and measurement of ecological productivity and related values;2) the role of stand history and disturbance in explaining forest characteristics;and 3) the interpretation of any relationship. We show that volume production and true productivity are distinct, and neither is a demonstrated proxy for economic values. Many stand characteristics, including diversity, volume growth and productivity, vary intrinsically with succession and stand history. We should be characterising these relationships rather than ignoring or eliminating them. Failure to do so may lead to misleading conclusions. To illustrate, we examine the study which prompted our concs—Liang et al. (Science 354:aaf8957, 2016)—which developed a sophisticated global analysis to infer a worldwide positive effect of biodiversity (tree species richness) onforest productivity(stand level wood volume production). Existing data should be able to address many of our concs. Critical evaluations will improve understanding.