I will discuss what we can learn about the different forms that Earth-like planetary atmospheres can take by studying Earth's paleoclimate records and fusing data with numerical models. Specifically, I will describe the geological evidence for the unusual dynamical state of 'greenhouse' climates that operated for much of Earth's history and use climate models to focus on understanding the physical balances that these different states. Most of the talk will be about the Eocene, a fascinating interval from 55 to 35 million years ago that began within one of the hottest intervals in Earth's history and ended with the initiation of Antarctic glaciation. Feedbacks, sensitivity, non-linearity, heat death, model-dependence, and baboons will all rear their ugly heads. I will extend this analysis to present some preliminary results that bear on the question of whether future climate might return to the 'greenhouse' state and what implications this has for the biosphere.