Structural variants (SVs) are large rearrangements (> 50 bp) within the genome that impact gene function and the content and structure of chromosomes. As a result, SVs are a significant source of functional genomic variation, i.e. variation at genomic regions underpinning phenotype differences, that can have large effects on individual and population fitness. While there are increasing opportunities to investigate functional genomic variation in threatened species via single nucleotide polymorphism (SNP) datasets, SVs remain understudied despite their potential influence on fitness traits of conservation interest. In this future-focused Opinion, we contend that characterizing SVs offers the conservation genomics community an exciting opportunity to complement SNP-based approaches to enhance species recovery. We also leverage the existing literature–predominantly in human health, agriculture and eco-evolutionary biology–to identify approaches for readily characterizing SVs and consider how integrating these into the conservation genomics toolbox may transform the way we manage some of the world’s most threatened species.