The number of alien plants escaping from cultivation into native ecosystems is increasing steadily. We provide an overview of the historical, contemporary and potential future roles of ornamental horticulture in plant invasions. We show that currently at least 75% and 93% of the global naturalised alien flora is grown in domestic and botanical gardens, respectively. Species grown in gardens also have a larger naturalised range than those that are not. After the Middle Ages, particularly in the 18th and 19th centuries, a global trade network in plants emerged. Since then, cultivated alien species also started to appear in the wild more frequently than non-cultivated aliens globally, particularly during the 19th century. Horticulture still plays a prominent role in current plant introduction, and the monetary value of live-plant imports in different parts of the world is steadily increasing. Historically, botanical gardens - an important component of horticulture - played a major role in displaying, cultivating and distributing new plant discoveries. While the role of botanical gardens in the horticultural supply chain has declined, they are still a significant link, with one-third of institutions involved in retail-plant sales and horticultural research. However, botanical gardens have also become more dependent on commercial nurseries as plant sources, particularly in North America. Plants selected for ornamental purposes are not a random selection of the global flora, and some of the plant characteristics promoted through horticulture, such as fast growth, also promote invasion. Efforts to breed non-invasive plant cultivars are still rare. Socio-economical, technological, and environmental changes will lead to novel patterns of plant introductions and invasion opportunities for the species that are already cultivated. We describe the role that horticulture could play in mediating these changes. We identify current research challenges, and call for more research efforts on the past and current role of horticulture in plant invasions. This is required to develop science-based regulatory frameworks to prevent further plant invasions.