This Element proposes to view World Englishes as components of an overarching Complex Dynamic System of Englishes, against the conventional view of regarding them as discrete, rule-governed, categorial systems. After outlining this basic idea and setting it off from mainstream linguistic theories, it introduces the theory of Complex Dynamic Systems and the main properties of such systems (systemness, complexity, perpetual dynamics, network relationships, the interplay of order and chaos, emergentism and self-organization, nonlinearity and fractals, and attractors), and surveys earlier applications to language. Usage-based linguistics and construction grammar are outlined as suitable frameworks to explain how the Complex Systems principles manifest themselves in linguistic reality. Many structural properties and examples from several World Englishes are presented to illustrate the manifestations of Complex Systems principles in specific features of World Englishes. Finally, the option of employing the NetLogo programming environment to simulate variety emergence via agent-based modeling is suggested.