In a minority of flowering plants, separate sexes are genetically determined by sex chromosomes. The Y chromosome has a non-recombining region that degenerates, causing a reduced expression of Y genes. In some species, the lower Y expression is accompanied by dosage compensation, a mechanism that re-equalizes male and female expression and/or brings XY male expression back to its ancestral level. Here, we review work on dosage compensation in plants, which started as early as the late 60s with cytological approaches. The use of transcriptomics fired a controversy as to whether dosage compensation existed in plants. Further work revealed that various plants exhibit partial dosage compensation, including a few species with young and homomorphic sex chromosomes. We are starting to understand the mechanisms responsible for DC in some plants, but in most species we lack the data to differentiate between global and gene-by-gene dosage compensation. Also, it is unknown why some species evolve many dosage compensated genes while others do not. Finally, the forces that drive DC evolution remain mysterious, both in plants and animals. We review the multiple evolutionary theories that have been proposed to explain DC patterns in eukaryotes with XY or ZW sex chromosomes.