Here, we leverage our cross-sector expertise in conservation (AWS, CJH, JG, JRW, KPK, MLL, SJG, TES), human health (DE), agriculture (JG), quantitative genetics (AWS) and bioinformatics (DE, JG, JRW, MLL) to consider the significance of SVs in population persistence and species extinction risk, and discuss opportunities and challenges for relating SVs to fitness traits in small populations. We identify approaches for reliably characterizing SVs with an emphasis on leveraging new and existing genomic resources for species of conservation concern. We also describe how the incorporation of genome assemblies for multiple reference individuals can be used to improve SV discovery and genotyping, even for large and/or complex SVs (Alonge et al., 2020; Eizenga et al., 2020; Gao et al., 2019; Golicz, Batley, & Edwards, 2016; Tettelin et al., 2005). We contend that the study of SVs has the potential to improve conservation outcomes by enhancing our understanding of genome-wide variation and traits related to fitness.