Many invasive plant species interfere with native plants through allelopathy.  A famous case of purported allelopathy is in desert shrubs. One of the most widely known early examples was Salvia leucophylla, because it was on the cover of the journal Science in 1964. Bare zones around the shrubs were hypothesized to be caused by volatile terpenes emitted by the shrubs. However, like many allelopathy studies, it was based on artificial lab experiments and unwarranted extrapolations to natural ecosystems. In 1970, Science published a study where caging the shrubs to exclude rodents and birds allowed grass to grow in the bare zones.
A detailed history of this story can be found in Halsey 2004.
Garlic mustard is another invasive plant species that may owe its success partly to allelopathy. Its success in North American temperate forests may be partly due to its excretion of glucosinolates like sinigrin that can interfere with mutualisms between native tree roots and their mycorrhizal fungi.
Allelopathy has been shown to play a crucial role in forests, influencing the composition of the vegetation growth, and also provides an explanation for the patterns of forest regeneration. The black walnut (Juglans nigra) produces the allelochemical juglone, which affects some species greatly while others not at all. However, most of the evidence for allelopathic effects of juglone come from laboratory assays and it thus remains controversial to what extent juglone affects the growth of competitors under field conditions. The leaf litter and root exudates of some Eucalyptus species are allelopathic for certain soil microbes and plant species. The tree of heaven, Ailanthus altissima, produces allelochemicals in its roots that inhibit the growth of many plants. Spotted knapweed (Centaurea) is considered an invasive plant that also utilizes allelopathy.
Another example of allelopathy is seen in Leucaena leucocephala, known as the miracle tree. This plant contains toxic amino acids that inhibit other plants’ growth but not its own species growth. Different crops react differently to these allelochemicals, so wheat yield decreases, while rice increases in the presence of L. leucocephala.
Capsaicin is an allelochemical found in many peppers that are cultivated by humans as a spice/food source. It is considered an allelochemical because it is not required for plant growth and survival, but instead deters herbivores and prevents other plants from sprouting in its immediate vicinity. Among the plants it has been studied on are grasses, lettuce, and alfalfa, and on average, it will inhibit the growth of these plants by about 50%. Capsaicin has been shown to deter both herbivores and certain parasites’ performance. Herbivores such as caterpillars show decreased development when fed a diet high in capsaicin.