Anthropogenic global change is rapidly driving Earth’s climate outside the range of variation known from direct measurements and there is growing concern that it might cause a system-level change in the biosphere within decades. The information preserved in the fossil record is increasingly perceived as a source of crucial information about the behavior of the Earth System in states beyond those known from direct observation, including non-catastrophic “background” change. Here I review some recent progress using mathematical and computational approaches to analyzing and simulating the complex, biased and incomplete fossil record and some of its underlying processes, including the gain and loss of biodiversity in relation to environmental change. It appears that restricting the analysis to the most common fossil species and genera of fossil land mammals may be used to amplify real trends in the noisy data, that the main ecological structure is well preserved and can be used to reconstruct ecosystem productivity and climate of the past, and that spatial as well as temporal resolution is good. Mathematical modeling suggests that biodiversity is both gained and lost primarily in the middle of existing phenotype space and that invasion of new environments proceeds through adaptation of pre-existing species.