Tomato (Solanum lycopersicum L.) domestication and later introduction into Europe resulted in a genetic bottleneck that reduced genetic variation. Crosses with other wild tomato species from the Lycopersicon clade can be used to increase genetic diversity and improve important agronomic traits such as stress tolerance. However, many species in the Lycopersicon clade have intraspecific and interspecific incompatibility, such as gametophytic self-incompatibility and unilateral incompatibility. In this review, we provide an overview of the known incompatibility barriers in Lycopersicon. We begin by addressing the general mechanisms self-incompatibility, as well as more specific mechanisms in the Rosaceae, Papaveraceae, and Solanaceae. Incompatibility in the Lycopersicon clade is discussed, including loss of self-incompatibility, species exhibiting only self-incompatibility and species presenting both self-compatibility and self-incompatibility. We summarize unilateral incompatibility in general and specifically in Lycopersicon, with details on the 'self-compatible x self-incompatible' rule, implications of self-incompatibility in unilateral incompatibility and self-incompatibility-independent pathways of unilateral incompatibility. Finally, we discuss advances in the understanding of compatibility barriers and their implications for tomato breeding.