Biological invasions create complex ecological and societal issues worldwide. Most of the knowledge about invasions comes only from successful invaders, but less is known about which processes determine the differential success of invasions. In this review, we develop a framework to identify the main dimensions driving the success and failure of invaders, including human influences, characteristics of the invader, and biotic interactions. We apply this framework by contrasting hypotheses and available evidence to explain variability in invasion success for 12 salmonids introduced to Chile. The success of Oncorhynchus mykiss and Salmo trutta seems to be influenced by a context-specific combination of their phenotypic plasticity, low ecosystem resistance, and propagule pressure. These well-established invaders may limit the success of subsequently introduced salmonids, with the possible exception of O. tshawytscha, which has a short freshwater residency and limited spatial overlap with trout. Although propagule pressure is high for O. kisutch and S. salar due to their intensive use in aquaculture, their lack of success in Chile may be explained by environmental resistance, including earlier spawning times than in their native ranges, and interactions with previously established and resident Rainbow Trout. Other salmonids have also failed to establish, and they exhibit a suite of ecological traits, environmental resistance, and limited propagule pressure that are variably associated with their lack of success. Collectively, understanding how the various drivers of invasion success interact may explain the differential success of invaders and provide key guidance for managing both positive and negative outcomes associated with their presence.