In this introductory chapter, we provide insights into the debates that inspired this volume. Our aim is to extend the boundaries of the concept societal interaction and discuss the conditions for universities to undertake such endeavors. Within this context, we introduce the matter of “mattering” which serves as the central theme that runs through this volume. Mattering, we posit, can be comprehended through three key concepts: collaboration, engagement, and impact. We outline how each concept contributes to an increasing understanding of the manifold ways in which mattering can be grasped and achieved. Furthermore, we provide an overview of the coherent set of individual chapters that, separately or jointly, deal with the three concepts. Through these chapters, this volume aims to make a valuable addition to the evolving literature that explores how universities can expand their impact beyond conventional higher education missions. Collectively, these chapters cover the context of the mattering of universities and draw on various empirical data sources, mainly from Sweden but also internationally. Within this compilation of inquiries, we shed light on the multifaceted impact of universities on societies, exploring the mechanisms, contexts, and temporal dimensions of their contributions to advancing knowledge and addressing societal challenges. © The Author(s) 2024.