Deletion, insertion, and duplications larger than 1 kb are structural variants (SVs) classified as copy number variants (CNVs). Beside single nucleotide variants (SNVs), CNVs are widespread in plants and substantially contribute to intra-species genetic variation. Most CNVs reported so far overlap with protein-coding sequences and result in gains or losses of gene copies that might directly influence transcript dosage. In several cases they proved to play an important role in the adaptive response of plants, by regulating development, and by increasing resistance to biotic and abiotic stresses. The advent of next-generation sequencing (NGS) is giving the possibility to uncover frequency and importance of CNVs. Although complexity of plant genomes and the short read length obtained from NGS platforms posed technical and computational challenges for their discovery, these are currently tackled with five strategies. New developments are expected, by third-generation NGS, the need for comprehensive databases, and the application in plant improvement.