A quick run through by Wikipedia:
A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts.[citation needed] This characteristic of every system is called emergence and is true of any system, not just complex ones[citation needed].
A system’s complexity may be of one of two forms: disorganized complexity and organized complexity.[1] In essence, disorganized complexity is a matter of a very large number of parts, and organized complexity is a matter of the subject system (quite possibly with only a limited number of parts) exhibiting emergent properties.
Examples of complex systems include ant colonies, human economies and social structures, climate, nervous systems, cells and living things, including human beings, as well as modern energy or telecommunication infrastructures. Indeed, many systems of interest to humans are complex systems.
Complex systems are studied by many areas of natural science, mathematics, and social science. Fields that specialize in the interdisciplinary study of complex systems includesystems theory, complexity theory, systems ecology, and cybernetics.