Climate proxy data provide noisy, and spatially incomplete information on some aspects of past climate states, whereas palaeosimulations with climate models provide global, multi-variable states, which may however differ from the true states due to unpredictable internal variability not related to climate forcings, as well as due to model deficiencies. Using data assimilation for combining the empirical information from proxy data with the physical understanding of the climate system represented by the equations in a climate model is in principle a promising way to obtain better estimates for the climate of the past. Data assimilation has been used for a long time in weather forecasting and atmospheric analyses to control the states in atmospheric General Circulation Models such that they are in agreement with observation from surface, upper air, and satellite measurements. Here we discuss the similarities and the differences between the data assimilation problem in palaeoclimatology and in weather forecasting, and present and conceptually compare three data assimilation methods that have been developed in recent years for applications in palaeoclimatology. All three methods (selection of ensemble members, Forcing Singular Vectors, and Pattern Nudging) are illustrated by examples that are related to climate variability over the extratropical Northern Hemisphere during the last millennium. In particular it is shown that all three methods suggest that the cold period over Scandinavia during 1790-1820 is linked to anomalous northerly or easterly atmospheric flow, which in turn is related to a pressure anomaly that resembles a negative state of the Northern Annular Mode.