In recent years Harmonia axyridis (Pallas, 1773) (Coleoptera: Coccinellidae) has become a very popular insect among biological control practitioners and scientists, not only for its potential to be an efficient biological control agent but also because it is considered invasive. Individuals of this species were deliberately introduced into several countries for biological control of different arthropods pests. However the predator itself became an invasive species, affecting the dynamics and composition of several guilds through direct or indirect interactions with established species, including intraguild predation. In this paper we discuss the reasons why the species has a high invasiveness and what are the limits to invasion by this species. It is not clear if the invasiveness of the beetle is linked to its biological, ecological and behavioural abilities, or to other factors such as invasibility and interactions between the invaders, the noninvaders, and the habitat, which may in part explain the reasons of its success and help us to answer the question ''what will stop the invader?'' We also discuss the reason for the absence of the predator in the Azores islands. Despite the intentional introduction of H. axyridis in the Azores and the high number of individuals released, there are no records of this species in the wild, despite recent extensive sampling effort. In this paper we discuss the reasons for the apparent failure or the delay in establishment of the predator. One factor which may hamper the establishment of H. axyridis in some of the Azores islands is the absence of winter