The Earth's climate is affected, among other factors, by the precession angle. Decrease of the precession angle is accompanied by a noticeable climate cool-down. As soon as Earth's average near-surface temperature reaches some critical value, glaciation emerges. The emergence and growth of ice covers unavoidably result in a distortion of Earth's spherical symmetry (its equilibrium revolution) causing relatively rapid increase in the precession angle. There is a good correlation between the theoretical and experimental data. These data indicate that the glaciations over the northern continents and the advent of the glaciation periods occurred after the average Earth's temperature declines below approximate to +10.5 degrees C to 10 degrees C. As a result of the interaction between the Moon and Earth during the Pleistocene time, slow but orderly climate cooling episodes occurred periodically. Their magnitude was 8 degrees C to 10 degrees C, and their duration reached 100,000 to 120,000 years. After a thick ice cover formed, the climate rapidly, during a few thousand years, warmed up by the same amount of 8 degrees C to 10 degrees C, and the glaciations degraded just as rapidly. Thus, that Moon-Earth interaction in combination with the glaciations induces substantially nonlinear self-oscillatory climatic processes, which are so typical for the entire Late Pleistocene time. In the future, despite the abundant release of anthropogenic gases, there will be a significant cooling down, possibly the most severe in the geologic history.