Climate warming and extended droughts drive establishment and growth dynamics in temperate grassland plants

•Central European grassland plants record climate changes in their radial growth rings.•Warmer and drier climate reduces plant growth and establishment.•Summer droughts adversely affect mainly the growth of shallow-rooted species.•Growth responses over the past thirty years were species-specific and related to life histories.•Herb-chronology provides in-depth insights into climate effects on plant fitness.