Links between climate and Earth’s orbit have been proposed for about 160 years. Two decisive advances towards an astronomical theory of palæoclimates were Milankovitch’s theory of insolation (1941) and independent findings, in 1976, of a double precession frequency peak in marine sediment data and from celestial mechanics calculations. The present chapter reviews three essential elements of any astronomical theory of climate: (1) to calculate the orbital elements, (2) to infer insolation changes from climatic precession, obliquity and eccentricity, and (3) to estimate the impact of these variations on climate. The Louvain-la-Neuve climate-ice sheet model has been an important instrument for confirming the relevance of Milankovitch’s theory, but it also evidences the critical role played by greenhouse gases during periods of low eccentricity. It is recognised today that climatic interactions at the global scale were involved in the processes of glacial inception and deglaciation. Three examples are given, related to the responses of the carbon cycle, hydrological cycle, and the terrestrial biosphere, respectively. The chapter concludes on an outlook on future research directions on this topic.