Chapter 2 describes the origins of complex dynamic systems theory (CDST) and explains the key concepts in this theory. Complex dynamic systems (CDSs) are characterised by heterogeneity, dynamism, non-linearity, openness, adaptation, and context-dependency. The CDST perspective on language development is described with reference to other non-symbolic theories, such as connectionism, emergentism, and usage-based theories, which stand in contrast to symbolic linguistic theories, such as nativism. Non-symbolic theories question the existence of an innate human endowment and reject inheritance and predeterminism as solutions to the logical problem of language acquisition, arguing that language development depends on general cognitive mechanisms applied to linguistic data. The CDST perspective is presented in terms of language and its evolution, first and second language development, and dynamic usage-based (DUB) instruction. This is followed by description of a general research paradigm which contrasts simplicity, determinism, and reductionism with restricted complexity, general complexity, and complex realism. The description also includes the different qualitative and quantitative methods recommended for CDST research. The scope of CDST research in second language acquisition (SLA) is characterised on the basis of substantive and methodological syntheses spanning two decades. Finally, CDST is critically evaluated for its contribution to applied linguistics.