Sex chromosomes are widespread in species with separate sexes. They have evolved many times independently, and display a truly remarkable diversity. New sequencing technologies and methodological developments have allowed the field of molecular evolution to explore this diversity in a large number of model and non-model organisms, broadening our vision on the mechanisms involved in their evolution. Diverse studies have allowed us to better capture the common evolutionary routes that shape sex chromosomes, however we still mostly fail to explain why sex chromosomes are so diverse. We review over half a century of theoretical and empirical work on sex chromosome evolution and highlight pending questions on their origins, turnovers, rearrangements, degeneration, dosage compensation, gene content, and rates of evolution. We also report recent theoretical progress on our understanding of the ultimate reasons for sex chromosomes' existence.