Structural variations (SVs) including gene presence/absence variations and copy number variations are a common feature of genomes in plants and, together with single nucleotide polymorphisms and epigenetic differences, are responsible for the heritable phenotypic diversity observed within and between species. Understanding the contribution of SVs to plant phenotypic variation is important for plant breeders to assist in producing improved varieties. The low resolution of early genetic technologies and inefficient methods have previously limited our understanding of SVs in plants. However, with the rapid expansion in genomic technologies, it is possible to assess SVs with an ever-greater resolution and accuracy. Here, we review the current status of SV studies in plants, examine the roles that SVs play in phenotypic traits, compare current technologies and assess future challenges for SV studies.