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The development of scientific ideas about the condensed state of matter has shown a pronounced trend: from studying the physicochemical properties of a wide class of objects using a quantum statistical approach (the first half of the XX century) to the interest in the role of structural characteristics, which began with the famous memorandum of R. Feynman -1958 (from "nano" to "fractality", "small dimension", "chirality" and "hierarchical structure"). In parallel, great achievements were used in studying the influence of the degree of disequilibrium of processes involving these objects. However, since the beginning of the XX century, there has been a conscious connection of physico-chemical knowledge with synergetic ideas of nonlinearity and disequilibrium. The increasing success of this compound took shape in the form of a new concept of CMP (condensed matter physics) – Complexity. Along the way, three types of qualitatively different paradigms were identified: self-organization, dynamic chaos and self-organized criticality, which allowed them to be guided naturally in solving the most modern problems of living and inanimate Nature, which gives hope for progress in identifying the unity of these two aspects of Nature. [ABSTRACT FROM AUTHOR]