Paleo data-model comparison is the process of comparing output from model simulations of past periods with paleoenvironmental data. It enables us to understand both the paleoclimate mechanism and responses of the earth environment to the climate and to evaluate how models work. This dissertation has two parts that each involve the development and application of approaches for data-model comparisons. In part 1, which is focused on the understanding of both past and future climatic changes/variations, I compare paleoclimate and historical simulations with future climate projections exploiting the fact that climate-model configurations are exactly the same in the paleo and future simulations in the Coupled Model Intercomparison Project Phase 5. In practice, I investigated large-scale temperature responses (land-ocean contrast, high-latitude amplification, and change in temperature seasonality) in paleo and future simulations, found broadly consistent relationships across the climate states, and validated the responses using modern observations and paleoclimate reconstructions. Furthermore, I examined the possibility that a small set of common mechanisms controls the large-scale temperature responses using a simple energy-balance model to decompose the temperature changes shown in warm and cold climate simulations and found that the clear-sky longwave downward radiation is a key control of the robust responses. In part 2, I applied the equilibrium terrestrial biosphere models, BIOME4 and BIOME5 (developed from BIOME4 herein), for reconstructing paleoclimate. I applied inverse modeling through the iterative forward-modeling (IMIFM) approach that uses the North American vegetation data to infer the mid-Holocene (MH, 6000 years ago) and the Last Glacial Maximum (LGM, 21,000 years ago) climates that control vegetation distributions. The IMIFM approach has the potential to provide more accurate quantitative climate estimates from pollen records than statistical approaches. Reconstructed North American MH and LGM climate anomaly patterns are coherent and consistent between variables and between BIOME4 and BIOME5, and these patterns are also consistent with previous data synthesis. This dissertation includes previously published and unpublished coauthored material.