Y chromosomes are genetically degenerate, having lost most of the active ge
nes that were present in their ancestors. The causes of this degeneration h
ave attracted much attention from evolutionary theorists. Four major theori
es are reviewed here: Muller's ratchet, background selection, the Hill-Robe
rtson effect with weak selection, and the 'hitchhiking' of deleterious alle
les by favourable mutations. All of these involve a reduction in effective
population size as a result of selective events occurring in a non-recombin
ing genome, and the consequent weakening of the efficacy of selection. Wie
review the consequences of these processes for patterns of molecular evolut
ion and variation at loci on Y chromosomes, and discuss the results of empi
rical studies of these patterns for some evolving Y-chromosome and neo-Y-ch
romosome systems. These results suggest that the effective population sizes
of evolving Y or neo-Y chromosomes are severely reduced, as expected if so
me or all of the hypothesized processes leading to degeneration are operati
ve. It is, however, currently unclear which of the various processes is mos
t important; some directions for future work to help to resolve this questi
on are discussed.