Lawsuits concerning the impacts of climate change make causal claims about the effect of defendants’ greenhouse gas (GHG) emissions on plaintiffs and have proliferated around the world. Plaintiffs have sought, inter alia, compensation for climate-related losses and to compel governments to reduce their GHG emissions. So far, most of these claims have been unsuccessful. Here we assess the scientific and legal bases for establishing causation and evaluate judicial treatment of scientific evidence in 73 lawsuits. We find that the evidence submitted and referenced in these cases lags considerably behind the state of the art in climate science, impeding causation claims. We conclude that greater appreciation and exploitation of existing methodologies in attribution science could address obstacles to causation and improve the prospects of litigation as a route to compensation for losses, regulatory action and emission reductions by defendants seeking to limit legal liability.