This book introduces complexity theory as a metaphor or supra-theory for systems in applied linguistics. Change and heterogeneity are central to complexity theory and to the resonances that we find with applied linguistics systems. Principles of complexity theory are explained, drawing on work in the biological, psychological and social sciences. These principles include descriptions of change over time (system dynamics) that work for all levels and scales: movement from temporary and relative stability through adaptive behaviours to the emergence of new patterns not amenable to reductive explanations. Seeing applied systems as complex, adaptive and dynamic opens up new conceptualisations of properties and activities, enables new questions about how people use, learn and teach languages, and demands new ways of investigating behaviour and development.