Wide hybridization is an important factor of angiosperm speciation and provides an introgression of genes between species. In experimental conditions, wide hybridization is used to increase the genetic diversity of cultivated plants. Since the emergence of reproductive barriers is of great importance for speciation, plants’ capacity for wide crosses is determined by the possibility of overcoming these barriers. This review discusses the main types of incompatibility in wide crossing plants, as well as the factors and methodological approaches that contribute to overcoming them. The role of Kr genes, which determine incompatibility between wheat and rye, is one of the examples of a prezygotic isolation mechanism. Postzygotic incompatibility may be associated with a highly pronounced genetic and epigenetic variability induced by wide crossings. The early stages of the postzygotic period are crucial for developing hybrid seeds due to an embryo’s death, including those associated with uniparental chromosome elimination in hybrid cells and abnormal development of the endosperm. The depression and lethality of F1 hybrids may be the result of interaction between complementary genes, which cause hybrid necrosis, hybrid chlorosis, and hybrid dwarfness. The causes of hybrid sterility are discussed. Nuclear-cytoplasmic interactions are regarded as one of the mechanisms of incompatibility in wide crosses. Reciprocal hybrids and alloplasmic lines are the main models for studying cytoplasm effects and nuclear-cytoplasmic interactions. Problems concerning work with their models are emphasized. There are some examples underlying the fact that alloplasmic lines are not a plain combination of the nuclear genome and cytoplasm of different species. The development of alloplasmic lines is connected with the structural and functional variability of nuclear and organelle genomes.