The question why non-avian dinosaurs went extinct 66 million years ago (Ma) remains unresolved because of the coarseness of the fossil record. A sudden extinction caused by an asteroid is the most accepted hypothesis but it is debated whether dinosaurs were in decline or not before the impact. We analyse the speciation-extinction dynamics for six key dinosaur families, and find a decline across dinosaurs, where diversification shifted to a declining-diversity pattern ~76 Ma. We investigate the influence of ecological and physical factors, and find that the decline of dinosaurs was likely driven by global climate cooling and herbivorous diversity drop. The latter is likely due to hadrosaurs outcompeting other herbivores. We also estimate that extinction risk is related to species age during the decline, suggesting a lack of evolutionary novelty or adaptation to changing environments. These results support an environmentally driven decline of non-avian dinosaurs well before the asteroid impact.