Many species are facing unprecedented population size declines and deterioration of their environment. This exposes species to genomic erosion, which we define here as the damage inflicted to a species' genome or gene pool due to a loss of genetic diversity, an increase in expressed genetic load, maladaptation, and/or genetic introgression. The International Union for Conservation of Nature (IUCN) bases its extinction risk assessments on direct threats to population size and habitat. However, it does not assess the long-term impacts of genomic erosion, and hence, it is likely to underestimate the extinction risk of many species. High-quality whole genome sequence data that is currently being generated could help improve extinction risk assessments. Genomic data contains information about a species' past demography, its genome-wide genetic diversity, the incidence of genetic introgression, as well as the genetic load of deleterious mutations. Computer modelling of these data enables forecasting of population trajectories under different management scenarios. In this Perspective, we discuss the threats posed by genomic erosion. Using evolutionary genomic simulations, we argue that whole-genome sequence data provides critical information for assessing species extinction risk and recovery potential. Genomics-informed assessments of the extinction risk complement the IUCN Red List, and such genomics-informed conservation is invaluable in guiding species recovery programs in the UN's Decade on Ecosystem Restoration and beyond.