The ASLAN labex - Advanced studies on language complexity - brings together a unique set of expertise and varied points of view on language. In this volume, we employ three main sections showcasing diverse empirical work to illustrate how language within human interaction is a complex and adaptive system. The first section - epistemological views on complexity - pleads for epistemological plurality, an end to dichotomies, and proposes different ways to connect and translate between frameworks. The second section - complexity, pragmatics and discourse - focuses on discourse practices at different levels of description. Other semiotic systems, in addition to language are mobilized, but also interlocutors' perception, memory and understanding of culture. The third section - complexity, interaction, and multimodality - employs different disciplinary frameworks to weave between micro, meso, and macro levels of analyses. Our specific contributions include adding elements to and extending the field of application of the models proposed by others through new examples of emergence, interplay of heterogeneous elements, intrinsic diversity, feedback, novelty, self-organization, adaptation, multi-dimensionality, indeterminism, and collective control with distributed emergence. Finally, we argue for a change in vantage point regarding the search for linguistic universals.