AbstractLarge particle accelerators are proposed as drivers for new ways to produce electricity from nuclear fusion and fission reactions. The accelerators must be designed to deliver high particle beam currents to a target facility with very little beam spill along the accelerator itself, in order that accelerator maintenance can be accomplished without remote manipulators. Typically, particle loss is preceded by the formation of a tenuous halo of particles around the central beam core, caused by beam dynamics effects, often coupled with the slight imperfections inevitable in a practical design. If the halo becomes large enough, particles may be scraped off along the accelerator. The tolerance for beam spill in different applications is discussed, halo mechanisms and recent work to explore and understand their dynamics are reviewed, and possible directions for future investigation are outlined.