Invasions by exotic species represent both threats to ecosystems as well as opportunities to learn more about them. Among the invaders that will have the largest impacts are those that directly modify ecosystems and thus have cascading effects for resident biota. Exotics can affect ecosystems by altering system-level flows, availability, or quality of nutrients, food, and physical resources (e.g. living space, water, heat or light). The invader-mediated control of physical resources, typically achieved through the modification of habitats, has received limited attention in invasion biology. This reflects a general trend in ecology, and only recently has the concept of ecosystem engineering been developed to account for the role of species that shape habitats. Plants and animals in terrestrial and aquatic systems can both create and destroy structure. When introduced into ecosystems, these exotic engineers cause physical state changes with effects that ramify throughout the system. Although the consequences of these modifications are varied and complex, insight gained from general ecological principles offers an opportunity to predict what invaders will do upon their integration into systems. Examples from the literature suggest that introduced ecosystem engineers that increase habitat complexity or heterogeneity tend to cause abundances and/or species richness to rise, while those that decrease complexity tend to have the reverse effect. In assessing such patterns, however, it is critical to also consider spatial scales and the life habits of resident organisms. In addition to providing predictive power, recognition of engineering as a major means by which invasive species affect ecosystems provides a unifying theme for invasion biology and offers a chance to consider more fully the general role of species in ecosystems.