The study of complexity has emerged out of a number of analytical trends in the physical and biological sciences in the last century, principally in the fields of computing and computer modelling, cybernetics, dynamical system theory (a branch of classical mechanics which studies the properties and interactions of many-bodied point mass systems), 'organismic' biology (an approach to theoretical biology emphasizing an analytic approach to vitalistic concepts such as teleology) and thermodynamics. In an attempt to provide modern scientific foundations for vitalistic notions such as teleological behaviour, analytic biologists such as Cannon and Sommerhoff proposed analytic or behavioural analyses and definitions of biological notions. Once given a behavioural grounding, these models were able to migrate out of biology, to account for analogical features of non-biological systems: first to the study of machines and control systems in cybernetics, and thence to a wide range of physical and social processes, aided by developments in non-linear dynamics such as dynamical systems theory, the emergence of the statistical sciences, and the development of modern computer modelling. Somewhat surprisingly, there has been little theoretical interaction between complexity theory and continuum mechanics, a part of classical mechanics that also deals with non-linear phenomena (such as elastic collisions or fluid flow), perhaps because complexity theory standardly deals with systems of discrete elements, and not homogenous continua. A consequence is that non-linearity may not be a sufficient characterization of complexity. ‘Complexity’ (a term that can describe behaviour and function equally well as structure) has since become a trans-disciplinary umbrella term that is intended to denote that feature of entities which is claimed to be responsible or to account for such characteristics, in both living and non-living systems. Complexity, as a concept, thereby provides not only analysis, but also (and perhaps more crucially, yet contentiously) a uniform explanation for the structure and behaviour of a very extensive range of phenomena. Philosophical problems associated with complexity include clarifying the meanings of various concepts associated with complexity, such as emergence, non-linearity, feedback, adaptation, and self-organization, and the extent to which these terms can be given scientific meaning, that is, the extent to which these terms can be meaningfully used in the physical sciences themselves. The study of complexity also naturally intersects with more traditional problem areas in the philosophy of the sciences, such as the study of reductionism, modelling, supervenience, functionalism, and causality; however the focus of contemporary philosophy of complexity has largely tended towards the examination of (or in many cases, an attempt at the legitimization of) a scientific grounding of a particular set of approaches to these problem areas. Much of this focus is surely due to the fact that the study of complexity in the twentieth century has largely been driven by scientific practitioners themselves, and not by philosophers or philosophers of science. As such, contemporary complexity theory also makes assumptions about the relationship between scientific and philosophical theories, leading to one of its central problems: its essential ambiguity. Is complexity science a specific branch of physical science (for example, the study of 'complex adaptive systems'); a study of a widespread trans-disciplinary scientific phenomenon (leading to the study of, for example, various broad 'measures of complexity', not to speak of complexity in other divisions of science, including biological and social complexity); or even a general (and allegedly paradigmatic) approach to science itself (the source of many popularizations, and in some cases works bordering on pseudo-science)? This ambiguity (which is reflected in the bibliography) opens up further avenues for exploration, and has implications for the manner in which philosophers should attempt to approach the subject.