Colloquium 657 - Recent Advances in Non-Smooth Dynamics (NSD2025) is a specialised forum dedicated to bringing together leading researchers, engineers, and industry professionals to explore the forefront of non-smooth dynamical systems. These systems, characterised by abrupt changes in behaviour, are increasingly pivotal across various engineering and technological applications. From mechanical linkages and automotive subsystems, such as gears and bearings, to flexible multibody systems like beams and cables, non-smooth dynamics present unique challenges and opportunities that are crucial to modern innovation.