Plants have a long evolutionary history, during which mass extinction events dramatically affected Earth's ecosystems and its biodiversity. The fossil record can shed light on the diversification dynamics of plant life and reveal how changes in the origination-extinction balance have contributed to shaping the current flora. We use a novel Bayesian approach to estimate origination and extinction rates in plants throughout their history. We focus on the effect of the 'Big Five' mass extinctions and on estimating the timing of origin of vascular plants, seed plants and angiosperms. Our analyses show that plant diversification is characterized by several shifts in origination and extinction rates, often matching the most important geological boundaries. The estimated origin of major plant clades predates the oldest macrofossils when considering the uncertainties associated with the fossil record and the preservation process. Our findings show that the commonly recognized mass extinctions have affected each plant group differently and that phases of high extinction often coincided with major floral turnovers. For instance, after the Cretaceous-Paleogene boundary we infer negligible shifts in diversification of nonflowering seed plants, but find significantly decreased extinction in spore-bearing plants and increased origination rates in angiosperms, contributing to their current ecological and evolutionary dominance.