Biological invasions contribute to global environmental change, but the dynamics and consequences of most invasions are difficult to assess at regional scales. We deployed an airborne remote sensing system that mapped the location and impacts of five highly invasive plant species across 221,875 ha of Hawaiian ecosystems, identifying four distinct ways that these species transform the three-dimensional (3D) structure of native rain forests. In lowland to montane forests, three invasive tree species replace native midcanopy and understory plants, whereas one understory invader excludes native species at the ground level. A fifth invasive nitrogen-fixing tree, in combination with a midcanopy alien tree, replaces native plants at all canopy levels in lowland forests. We conclude that this diverse array of alien plant species, each representing a different growth form or functional type, is changing the fundamental 3D structure of native Hawaiian rain forests. Our work also demonstrates how an airborne mapping strategy can identify and track the spread of certain invasive plant species, determine ecological consequences of their proliferation, and provide detailed geographic information to conservation and management efforts.