Climate research is constrained by the practical impossibility of experimenting with the climate system to test hypotheses and the limited length of observations, which usually hampers a thorough statistical analysis. This is one of the reasons why paleoclimatology, the study of past climate variations can give valuable insights about present climate change and put this change against a broader background. However, palaeoclimatology needs to rely on indirect evidence, so-called proxy data, which contains information about past environmental conditions and needs to be adequately interpreted. Often, this interpretation requires rather sophisticated statistical analysis. This chapter presents four important contributions to paleoclimatology that arose within the Hamburg climate network. Three of them analyze available indirect observations to infer past climate variations in the recent past and also at longer glacial timescales. The fourth contribution is more methodological and focused on ways to test statistical climate reconstruction methods using synthetic data.