The world's forests face unprecedented threats from invasive insects and pathogens that can cause large irreversible damage to the ecosystems. This threatens the world's capacity to provide long‐term fiber supply and ecosystem services that range from carbon storage, nutrient cycling, and water and air purification, to soil preservation and maintenance of wildlife habitat. Reducing the threat of forest invasive alien species requires vigilant biosurveillance, the process of gathering, integrating, interpreting, and communicating essential information about pest and pathogen threats to achieve early detection and warning and to enable better decision‐making. This process is challenging due to the diversity of invasive pests and pathogens that need to be identified, the diverse pathways of introduction, and the difficulty in assessing the risk of establishment. Genomics can provide powerful new solutions to biosurveillance. The process of invasion is a story written in four chapters: transport, introduction, establishment, and spread. The series of processes that lead to a successful invasion can leave behind a DNA signature that tells the story of an invasion. This signature can help us understand the dynamic, multistep process of invasion and inform management of current and future introductions. This review describes current and future application of genomic tools and pipelines that will provide accurate identification of pests and pathogens, assign outbreak or survey samples to putative sources to identify pathways of spread, and assess risk based on traits that impact the outbreak outcome.