Climate change arises from natural and anthropogenic external forcing, as well as from variations within the climate system. Whereas synoptic to interannual variations in the climate system are well observed and current climate models are generally able to simulate them realistically, much less is known about the amplitude and the mechanisms of climate variability on longer time-scales. Estimating that variability is the basis for the detection and attribution of the anthropogenic component and determines the range of plausible future climate changes. Imprints created during past environmental changes (proxies) as stable isotopes preserved in ice, terrestrial bio-indicators from lake sediments or marine proxies preserved in the sea sediment could provide this information, but are inherently noisy and often inconsistent to each other. This hampered quantitative reconstructions of climate variability and systematic testing of climate model simulations. Bridging the gap between the geological data, proxy processes and climate models, my research team works towards a quantitative approach for the use of proxy data to reconstruct climate variability. This includes a better understanding of paleoclimate proxies i.e. how climate variations get recorded in the geochemical record; statistical-physical models of the signal formation and the refinement of statistical techniques to infer climate variability from imperfect datasets. Based on these advances we were able to improve our understanding of climate variability in the Holocene and other time-periods.