In recent years, the world scientific community has been trying to combine their efforts to coordinate scientific research in the direction of complex system study. Thus, already in the 1980s, a special scientific discipline called complexity theory emerged. The science about complex nonlinear processes (Nonlinear Science, Science of complexity, Science of Chaos) is now only in the initial stage of rapid growth, as evidenced by the rapid development of this industry in the United States. The problems of complex nonlinear systems are studied at all major universities in Europe and America. This work is devoted to the analysis of various approaches to the study of complex system problem from modern positions. The issues of the systemic world development are covered briefly. They described the foundations of the modern understanding of global Evolutionism.