Predictions for modern global warming resulting from increased CO₂ levels have caused a heightened interest in the mechanics of ancient warm climates and especially of geologically abrupt warming events. Certain key intervals of the Cretaceous and Paleogene marked by rapid climate change are significant to current Earth science objectives because focused research has the potential to considerably improve our understanding of the general dynamics of the Earth during rapid perturbation of carbon cycle. These intervals mainly include: the Paleocene-Eocene Thermal Maximum (PETM, ~55 Ma) and Oceanic Anoxic Events (OAEs) in the late early Aptian (OAE1a，Selli Level, ~120 Ma) and at the Cenomanian-Turonian Boundary (OAE2, Bonarelli Level, ~93.5 Ma). Known as one of the most extreme and abrupt warming episodes since the mid-Cretaceous, the PETM is characterized by a rapid ~5℃ increase in deep ocean, about 4 to 8℃ increase in surface ocean, and a prominent negative carbon isotope excursion of at least 3.0‰ in less than 10 ka. One plausible explanation for the observed PETM  δ¹³C excursion involves massive release of CH₄ from gas hydrates in the ocean. The OAEs represent major perturbations of the ocean system defined by massive deposition of organic matter in marine environments. Integrated Ocean Drilling Program (IODP) includes the extreme climates as one of major scientific objectives. World-wide oceans with the minimal diagenesis in Cretaceous and Cenozoic sediments will be drilled by special drilling strategies to yield critical information of our understanding of these climatic extremes under a Milankovitch astronomically-calibrated time scale. The end is fundamental to a quantitative description of global change.