Large particle accelerators are proposed as drivers for new ways to pr
oduce electricity from nuclear fusion and fission reactions. The accel
erators must be designed to deliver high particle beam currents to a t
arget facility with very little beam spill along the accelerator itsel
f, in order that accelerator maintenance can be accomplished without r
emote manipulators. Typically, particle loss is preceded by the format
ion of a tenuous halo of particles around the central beam core, cause
d by beam dynamics effects, often coupled with the slight imperfection
s 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, an
d possible directions for future investigation are outlined.