Complex system theory is a new and rapidly- developing field. A complex system is composed of many simple individual components that interact nonlinearly, giving rise to global behaviors and often unexpected, unprecedented and unpredictable that exhibit nontrivial emergent and self-organizing behaviors. In this context, a sub-domain has emerged under the name “complex adaptive systems: CASâ€. This current coming from the developments in evolutionary algorithms in 1980 years, focused on complex systems in relation with an environment in which they dynamically learn and adapt. The goal of this work is to explore the Complex system theory through a comprehensive survey, which clearly shows the properties, the mechanisms, the applications, and the different scientific currents that are related to the complex systems from 1940 until 2015.We present the effective approach for modeling and simulating complex systems. We undertake a fairly exhaustive and rigorous survey of applications of complex theory in various domains of science.