The past 3.2 Myr have seen drastic climate changes with the development, waxing and waning of huge continental ice sheets over the Northern Hemisphere. These striking phenomena have been observed in various records from ice cores, as well as marine and terrestrial sediments. These proxy records showed periodicities associated with the three orbital parameters that affect our planet's insolation, namely eccentricity, obliquity and precession. Until recently, these periodicities were considered as the canonical ones for the Quaternary Period and beyond. However, the improvement of the time resolution of available records has allowed one to describe climate changes occurring abruptly and with periodicities that are not related to those of the orbital parameters. In this paper, we show that, in fact, these abrupt climate changes may still be related, albeit indirectly, to the astronomical theory of climate.