This mini-colloquium provides a forum to share the latest developments in theory, experiment and material synthesis on bound states arising in hybrid superconducting nanostructures. Such bound states, running under the flavours of Andreev bound states, Yu-Shiba-Rusinov states and Majorana bound states have the fundamental significance to describe and understand nanoscale superconductivity and to explore the latter’s potential for emerging quantum technologies. This prospect has spurred a great deal of efforts in recent years towards their creation and manipulation in various solid state platforms, including semiconductor nanowires, planar heterostructures, implanted adatoms, cavities, and quantum dot chains. This event is intended to provide a compact but comprehensive coverage of the current activities in this diverse and very active field of research.