Focused ion beam (FIB) machining promises exciting new possibilities for the study of quantum materials through precise control over the shape and geometry of single crystals on the submicrometer scale. It offers viable routes to fabricate high-quality mesoscale structures from materials that cannot yet be grown in thin-film form and to enhance the experimentally accessible signatures of new physical phenomena. Prototype devices can also be produced in a silicon-chip environment to investigate directly the materials application potential for future electronics. This review introduces the concepts of ion beam shaping of matter, discusses the role and extent of surface damage and material disorder inherent to these techniques, and gives an overview of recent experiments on FIB-structured crystals. Given the early stage of the field of FIB-fabricated quantum materials, much is yet to come, and emergent trends and future directions are also discussed.