An introduction to proxy data, paleoclimate databases, and data assimilation is presented. The reconstruction of paleoclimate fields is the defining measure for evaluation of climate change with respect to the modern transition from primarily natural variability forcing to anthropogenic forcing. This section focuses on proxy system modelling (PSM) and paleoclimate data assimilation (PDA) methods to merge objective numerical analysis of paleo-synoptic data with numerical-model hindcasts of paleoclimate. Prior to PDA, paleoclimate reconstructions were based upon regression models, principal component analysis (PCA), and Bayesian hierarchial models. These have limitations where data is sparse, and the PCA method relies on implied teleconnections. The PSM and PDA methods are designed to address these issues and model the uncertainty in reconstructions derived from the paleoclimate archive. Both statistical and process-based PSM methods are presented, as are recent applications. Kalman filtering and analogue-data modelling methods are presented as the methods most widely used for paleoclimate data assimilation, together with last millennial examples.