Predicting the consequences of climate change for biodiversity is critical to conservation efforts. Extensive range losses have been predicted for thousands of individual species, but less is known about how climate change might impact whole clades and landscape-scale patterns of biodiversity. Here, we show that climate change scenarios imply significant changes in phylogenetic diversity and phylogenetic endemism at a continental scale in Australia using the hyper-diverse clade of eucalypts. We predict that within the next 60 years the vast majority of species distributions (91%) across Australia will shrink in size (on average by 51%) and shift south on the basis of projected suitable climatic space. Geographic areas currently with high phylogenetic diversity and endemism are predicted to change substantially in future climate scenarios. Approximately 90% of the current areas with concentrations of palaeo-endemism (that is, places with old evolutionary diversity) are predicted to disappear or shift their location. These findings show that climate change threatens whole clades of the phylogenetic tree, and that the outlined approach can be used to forecast areas of biodiversity losses and continental-scale impacts of climate change.