Leafminers are a taxonomically diverse group of endophagous insects. A number of them are pests in forestry, horticulture and agriculture, and some of them have become important invasive species. Here, we discuss the characteristics of invasive leafminers of woody plants. We first present 12 cases of invasive leaf-mining species belonging to four different insect orders. For each of them, we briefly describe their invasion, including pathways of introduction, their impact and management methods and their ecology. We then discuss various aspects of these invasions. Leafminers are introduced to new continents and spread through various pathways such as horticultural trade and accidental transport of adults and pre-imaginal stages in containers and vehicles. They may also spread long distances with air currents. A few species have serious economic impacts as orchard pests, such as the citrus leafminer, Phyllocnistis citrella, or as pests of ornamental plants, such as the horse-chestnut leafminer, Cameraria ohridella. The ecological impact of these species should be better studied, especially those killing native trees, such as the birch leaf-mining weevil, Orchestes fagi, in Canada. Compared to other insect groups, invasive leafminers are usually recruited by a range of native parasitoids, which may or may not succeed in controlling the invasive species. Biological control by introduction of parasitoids from the native range has often been successful to control invasive leafminers. The review ends by short discussions on taxonomic issues and on the use of leafminers as models to study invasion ecology.