ABSTRACT - Background:Self-incompatibility (SI) systems prevent self-fertilization in several species of Poaceae, many of which are economically important forage, bioenergy and turf grasses. Self-incompatibility ensures cross-pollination and genetic diversity but restricts the ability to fix useful genetic variation. In most inbred crops it is possible to develop high-performing homozygous parental lines by self-pollination, which then enables the creation of F1 hybrid varieties with higher performance, a phenomenon known as heterosis. The inability to fully exploit heterosis in outcrossing grasses is partially responsible for lower levels of improvement in breeding programmes compared with inbred crops. However, SI can be overcome in forage grasses to create self-compatible populations. This is generating interest in understanding the genetical basis of self-compatibility (SC), its significance for reproductive strategies and its exploitation for crop improvement, especially in the context of F1 hybrid breeding. Scope:We review the literature on SI and SC in outcrossing grass species. We review the currently available genomic tools and approaches used to discover and characterize novel SC sources. We discuss opportunities barely explored for outcrossing grasses that SC facilitates. Specifically, we discuss strategies for wide SC introgression in the context of the Lolium-Festuca complex and the use of SC to develop immortalized mapping populations for the dissection of a wide range of agronomically important traits. The germplasm available is a valuable practical resource and will aid understanding the basis of inbreeding depression and hybrid vigour in key temperate forage grass species. Conclusions:A better understanding of the genetic control of additional SC loci offers new insight into SI systems, their evolutionary origins and their reproductive significance. Heterozygous outcrossing grass species that can be readily selfed facilitate studies of heterosis. Moreover, SC introduction into a range of grass species will enable heterosis to be exploited in innovative ways in genetic improvement programmes. © 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Annals of Botany Company.