Spinach (Spinacia oleracea) is a dioecious species (with male and female flowers on separate individuals). Spinach and its closest wild relative,S. turkestanica, has homomorphic sex chromosomes, but the more distant relativeS. tetrandrahas heteromorphic sex chromosomes. We report high-quality genome assemblies forS. turkestanicaandS. tetrandra. These diverged approximately 6.3 million years ago (Mya), whileS. turkestanicasplit fromS. oleraceamuch more recently, around 0.8 Mya, supporting previous suggestions thatS. turkestanicais the direct progenitor of cultivated spinach. Using a combination of genomic approaches, we identified a sex-linked region (SLR) of ∼133 Mb inS. tetrandra. In all three species, the SLRs are within a large pericentromeric region of chromosome 4. We describe evidence that, inS. tetrandra, this region has completely stopped recombining in male meiosis, creating a large Y-linked region (YLR) that has partially degenerated; loss of recombination appears to have evolved in two events that created two “evolutionary strata”, one of which and is highly rearranged, relative to the X. The SLRs ofS. turkestanicaandS. oleraceaare much smaller: both include only a 10 Mb Y-specific region which is not detected inS. tetrandra. This was duplicated into a 14 Mb inverted region, and is termed the Y-duplicated region, or “YDR”. These findings suggest that a turnover event created the YDR before these species diverged, replacing an extensive ancestral Y-linked region like theS. tetrandraYLR.