We review some recently published results on sex chromosomes in a diversity of species. We focus on several fish and some plants whose sex chromosomes appear to be 'young', as only parts of the chromosome are nonrecombining, while the rest is pseudoautosomal. However, the age of these systems is not yet very clear. Even without knowing what proportions of their genes are genetically degenerate, these cases are of great interest, as they may offer opportunities to study in detail how sex chromosomes evolve. In particular, we review evidence that recombination suppression occurs progressively in evolutionarily independent cases, suggesting that selection drives loss of recombination over increasingly large regions. We discuss how selection during the period when a chromosome is adapting to its role as a Y chromosome might drive such a process.