The application of FISH chromosome painting techniques, especially the recent mFISH (and its equivalents) where all 23 human chromosome pairs can be distinguished, has demonstrated that many chromosome-type structural exchanges are much more complicated (involving more "break-rejoins" and arms) than has hitherto been assumed. It is clear that we have been greatly under-estimating the damage produced in chromatin by such agents as ionising radiation. This article gives a brief historical summary of observations leading up to this conclusion, and after outlining some of the problems surrounding the formation of complex chromosomes exchanges, speculates about possible solutions currently being proposed.