Progressive recombination loss is a common feature of sex chromosomes. Yet, the evolutionary drivers of this phenomenon remain a mystery. For decades, differences in trait optima between sexes (sexual antagonism) have been the favoured hypothesis, but convincing evidence is lacking. Recent years have seen a surge of alternative hypotheses to explain progressive extensions and maintenance of recombination suppression: neutral accumulation of sequence divergence, selection of nonrecombining fragments with fewer deleterious mutations than average, sheltering of recessive deleterious mutations by linkage to heterozygous alleles, early evolution of dosage compensation, and constraints on recombination restoration. Here, we explain these recent hypotheses and dissect their assumptions, mechanisms, and predictions. We also review empirical studies that have brought support to the various hypotheses.