This Research Topic originates from the symposium Probing Out-of-Equilibrium Soft Matter that was held on October 22–23, 2021 at the University of Fribourg (Switzerland) to celebrate and honor the career of Véronique Trappe (https://orcid. org/0000-0002-0301-258X). The symposium assembled leading scientists in the rapidly growing field of non-equilibrium soft matter physics, a field to which V. Trappe has made key contributions that have changed the view of many [1–6]. While the equilibrium behaviour of soft matter is amply studied and understood, novel tools are needed to capture the complexity of out-of-equilibrium soft materials. A particular challenge is getting access to and understanding the fast processes occurring at the nano-and micro-scale of the elementary constituents, while simultaneously capturing the slower evolution of bulk properties in non-equilibrium conditions. To take on this task, new theoretical, numerical and experimental methodologies need to be developed that enable the investigation of the structure, dynamics, thermodynamics, and rheology of out-of-equilibrium soft matter. Adopting a comprehensive view that covers fundamental topics as well as research focusing on processes and issues faced in applications, this Research Topic aims to showcase some of the latest advancements and innovations in the field.Living and active materials are intrinsically non-equilibrium systems due to metabolic activity and/or energy consumption. Using newly developed fabrication and image processing tools, Chang et al. probe the effect of surface curvature on the proliferation of Madin-Darby Canine Kidney (MDCK) epithelial …