When faced with multiple introductions of allogenic species in all ecosystems of the earth and with the risk that these introduced species become pests, ecological theory still shows a limited predictive power. During the last years, significant advances have been performed, particularly on a conceptual ground. Modelling and accurate factorial experiments have produced results that do not always converge with intuitive insights. Species richness and disturbance rate are not always related to naturalization of an allogenic species. The role of demographic factors (propagule rains, repetition of introductions, boom-and-bust) has not been sufficiently considered. Establishing lists of species that risk to become invasive remains a goal that can benefit by new approaches crossing phylogenetic factors, life history strategies and functional roles of the allogenic species in their native biocenoses. Hybridization, genomic introgression and lateral transfers of genetic material that result from introductions of allogenic species arouse a great interest, and all the more so as the marketing of genetically engineered organisms sets the problem at a wide scale. With regard to ecosystems, the impacts of invasions on the services provided by the ecosystems to human societies has not always been objectively assessed. Improving such an assessment implies to take into account the need for preserving biodiversity when the introduction of an alien threaten the viability of a native population. All these topics open important research perspectives for the next years.