James Croll was a pioneer in studies of the impact of the slowly changing orbital dynamics of the Earth on climate change. His book Climate and Time in their Geological Relations (1875) was far ahead of its time in seeking correlations between climate change, the occurrence of ice ages and perturbations to the Earth's orbit about the Sun. The astronomical cycles he discovered are now called ‘Milankovitch Cycles’ after the Serbian scientist whose research was first published in the Handbuch der Klimatologie in 1930. The celestial mechanical and astronomical background to Croll's research is the focus of this essay. The development of the understanding of the impact of perturbations of the elliptical planetary orbits by other bodies in the solar system paralleled new mathematical techniques, many of which were developed in association with celestial mechanical problems. The central contributions of many of the major mathematicians of the late 18th and 19th Centuries, including Euler, Lagrange, Laplace and Le Verrier, are highlighted. Although Croll's contributions faded from view for several generations, his pioneering insights have now been demonstrated to have been basically correct.