Given the inherent uncertainties in predicting how climate and environments will respond to anthropogenic emissions of greenhouse gases, it would be beneficial to society if science could identify geological analogues to the human race's current grand climate experiment. This has been a focus of the geological and palaeoclimate communities over the last 30 years, with many scientific papers claiming that intervals in Earth history can be used as an analogue for future climate change. Using a coupled ocean-atmosphere modelling approach, we test this assertion for the most probable pre-Quaternary candidates of the last 100 million years: the Mid- and Late Cretaceous, the Palaeocene-Eocene Thermal Maximum (PETM), the Early Eocene, as well as warm intervals within the Miocene and Pliocene epochs. These intervals fail as true direct analogues since they either represent equilibrium climate states to a long-term CO(2) forcing--whereas anthropogenic emissions of greenhouse gases provide a progressive (transient) forcing on climate--or the sensitivity of the climate system itself to CO(2) was different. While no close geological analogue exists, past warm intervals in Earth history provide a unique opportunity to investigate processes that operated during warm (high CO(2)) climate states. Palaeoclimate and environmental reconstruction/modelling are facilitating the assessment and calculation of the response of global temperatures to increasing CO(2) concentrations in the longer term (multiple centuries); this is now referred to as the Earth System Sensitivity, which is critical in identifying CO(2) thresholds in the atmosphere that must not be crossed to avoid dangerous levels of climate change in the long term. Palaeoclimatology also provides a unique and independent way to evaluate the qualities of climate and Earth system models used to predict future climate.