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The distinction between complicated and complex systems is of immense importance, yet it is often overlooked. Decision-makers commonly mistake complex systems for simply complicated ones and look for solutions without realizing that ‘learning to dance’ with a complex system is definitely different from ‘solving’ the problems arising from it. The situation becomes even worse as far as modern social systems are concerned. This article analyzes the difference between complicated and complex systems to show that (1) what is at stake is a difference of type, not of degree; (2) the difference is based on two different ways of understanding systems, namely through decomposition into smaller parts and through functional analysis; (3) complex systems are the generic, normal case, while complicated systems are highly distinctive, special, and therefore rare.