Combining palaeontological and neontological data offers a unique opportunity to investigate the relative roles of biotic and abiotic controls of species diversification, and the importance of origination versus extinction in driving evolutionary dynamics. Ferns comprise a major terrestrial plant radiation with an extensive evolutionary history providing a wealth of modern and fossil data for modelling environmental drivers of diversification. Here we develop a novel Bayesian model to simultaneously estimate correlations between diversification dynamics and multiple environmental trajectories. We estimate the impact of different factors on fern diversification over the past 400 million years by analysing a comprehensive dataset of fossil occurrences and complement these findings by analysing a large molecular phylogeny. We show that origination and extinction rates are governed by fundamentally different processes: originations depend on within-group diversity but are largely unaffected by environmental changes, whereas extinctions are strongly affected by external factors such as climate and geology. Our results indicate that the prime driver of fern diversity dynamics is environmentally driven extinction, with origination being an opportunistic response to diminishing ecospace occupancy.