In recent years, there has been a new interest in evaluating ‘complex’ structures in languages. The implications of such studies are varied, e.g., the distinction between supposedly more complex and less complex languages, how complexity relates to human knowledge of language, and the role of the reduction or increase of complexity in language change and creolization. This book focuses on the latter issue, but the conclusions presented here hold of typological ‘complexity’ in general. The chapters in this book show that the notion of complexity as conceived of in linguistics mainly centres on the outer manifestations of language (e.g., numbers of affixes). This exercise is useful in establishing the patterning of languages in terms of their degrees of analyticity or synthesis, but it fails to address the properties of the inner rules of these grammars, and how these relate to the computational system that governs the human language capacity. This means that issues of complexity should not be equated with the complexity observed in surface patterns of grammars alone.