Risk analysis of species invasions links biology and economics, is increasingly mandated by international and national policies, and enables improved management of invasive species. Biological invasions proceed through a series of transition probabilities (i.e., introduction, establishment, spread, and impact), and each of these presents opportunities for management. Recent research advances have improved estimates of probability and associated uncertainty. Improvements have come from species-specific trait-based risk assessments (of estimates of introduction, establishment, spread, and impact probabilities, especially from pathways of commerce in living organisms), spatially explicit dispersal models (introduction and spread, especially fr...