Abstract <p>A new system of statistical and stochastic estimates was proposed and used to analyze changes in the total mass of mountain glaciers in the world for 1930–2019, changes in the average mass of mountain glaciers in typical mountain-glacial regions of the world (Alaska Range, northern Scandinavia, Spitsbergen, the Alps, the Caucasus, Central Asia), changes in the mass of individual glaciers, as well as the runoff of glacier-fed rivers. It was shown that, along with the “greenhouse” trend in changes in the mass of mountain glaciers (both in global averaging and on average for the analyzed mountain-glacial regions and for specific glaciers), Wiener-type processes play a significant role—in accordance with the theory of stochastic models of natural climate change by K. Hasselmann. An increase in the variation coefficients of the annual, maximum, and minimum runoff of glacier-fed rivers, as well as an increase in the autocorrelation of the annual and maximum runoff with a decrease in the size of glaciers, are demonstrated. As glaciers degrade, one can expect an increase in the proportion of first-order autoregressive models to describe interannual changes in the runoff of these species and a decrease in the proportion of zero-order models.</p>