Cenozoic temperature, sea level and CO2 co-variations provide insights into climate sensitivity to external forcings and sea level sensitivity to climate change. Climate sensitivity depends on the initial climate state, but potentially can be accurately inferred from precise paleoclimate data. Pleistocene climate oscillations yield a fast-feedback climate sensitivity 3 +/- 1°C for 4 W/m2 CO2 forcing if Holocene warming relative to the Last Glacial Maximum (LGM) is used as calibration, but the error (uncertainty) is substantial and partly subjective because of poorly defined LGM global temperature and possible human influences in the Holocene. Glacial-to-interglacial climate change leading to the prior (Eemian) interglacial is less ambiguous and implies a sensitivity in the upper part of the above range, i.e., 3-4°C for 4 W/m2 CO2 forcing. Slow feedbacks, especially change of ice sheet size and atmospheric CO2, amplify total Earth system sensitivity by an amount that depends on the time scale considered. Ice sheet response time is poorly defined, but we show that the slow response and hysteresis in prevailing ice sheet models are exaggerated. We use a global model, simplified to essential processes, to investigate state-dependence of climate sensitivity, finding an increased sensitivity towards warmer climates, as low cloud cover is diminished and increased water vapor elevates the tropopause. Burning all fossil fuels, we conclude, would make much of the planet uninhabitable by humans, thus calling into question strategies that emphasize adaptation to climate change.