It is paradoxical that exotic species invade and displace native species that are well adapted to local environments. Yet, even those exotics that eventually become abundant and widespread, often do so only after having failed to establish following multiple earlier introductions. The first pattern, while not generally discussed in this context, is usually explained by exotic species pre-adaptations for human-altered environments and by a release from enemies. It can be understood further by examining the superior quality of colonists from large species-rich regions and the historical contingency of evolution. The second pattern is generally explained by invoking demographic and environmental stochasticity; however, it can be understood further by examining the role of environmental variation over space and by metapopulation dynamics. These processes provide a context in which these patterns of invasion are not paradoxical, but instead, expected.