What determines species diversity is one of the top 25 questions pointed out by Science to be resolved by scientists in the coming decades. Understanding what shapes diversity will require a major interdisciplinary effort, involving paleontological interpretation, field studies, laboratory experimentation, genomic analysis, and effective statistical analyses. Together, these efforts will go a long way toward clarifying the history of life. Figuring out what shapes diversity could be important for understanding the nature of the wave of extinctions the world is experiencing and for determining strategies to mitigate it. In this context, I will summarize my recent research on the relationships between climate change, global diversity patterns and past and future extinctions, at different spatial and temporal scales under a multidisciplinary framework that encompasses disciplines as Climatology, Biogeography and Global Change Biology.