The author describes the shastic (probabilistic) approach to the study of changes in the climate system. Climatic data and theoretical considerations suggest that a large part of climatic variation/variability has a random nature and can be analyzed using the theory of shastic processes. This work summarizes the results of processing existing records of climatic parameters as well as appropriate theories: from the theory of random processes (based on the results of Kolmogorov and Yaglom) and Hasselmann's "shastic climate model theory" to recently obtained results.