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We present a brief essay about the statistical physics of complex systems - a research direction that now acquires features of a well established field of science with its object of study, conceptual background, and methods of analysis. A complex system consists of many interacting parts (agents) and manifests collective behaviour nontrivially following from the behaviour of its individual components. Examples of complex systems are found in condensed matter, ecological and biological systems, human society, stock markets and economy. The concept of a complex system refers to many traditional disciplines of science and forms a new, inter-disciplinary branch of knowledge. Peculiar features of complex systems are self-organization, emergence of new functionalities, adaptive nature of interactions, high sensitivity to small changes in the initial conditions, governing power laws ("fat-tailed" distributions). In our paper, we concentrate on applying methods and concepts of statistical physics in a complex system analysis. We discuss how such approach allows for conceptual understanding and interpretation of a wide range of phenomena in various systems, not necessarily of physical origin. Together with the general description of the properties of complex systems, we give a brief overview of some studies performed in this field at the Institute for Condensed Matter Physics of the NAS of Ukraine (Lviv, Ukraine). In particular, these studies cover critical behaviour of complex magnets, scaling behaviour of complex polymer macromolecules, phase transition of spin system on complex networks, sociophysical approaches to studying human activities, scientometrics. [ABSTRACT FROM AUTHOR]