The CRISPR/Cas system is the most promising among genome editing tools. It can provide the development of modified nontransgenic plants with the possibility of simultaneous multiple targeted mutations. The purpose of this review is to analyze published papers describing the utilization of the CRISPR/Cas system for crop gene modification in order to assess the potential of this technology as a new plant breeding technique. The search for "CRISPR & crop name" within article titles, abstracts and keywords in the Scopus database was carried out for 45 crops. Among a total of 206 search results, only 88 have been recognized as original articles describing editing crop genes with the CRISPR/Cas system. A total of 145 target genes of 15 crops are described in these 88 articles, including rice with the largest number of genes modified (78 genes). In these studies, the ability to get transgene-free modified plants was widely demonstrated. However, in most cases research was aimed at the approbation of the technology or was to elucidate target gene function, while modification of just 37 target genes was related with crop improvement. We present here a catalogue of these genes. In most of these cases, modifications resulted in knockout of the genes such as negative growth and development regulators or negative regulators of plant resistance. In most cases, the phenotype of modified plants was assessed, and the presence of desired changes was shown. However, since the estimated number of "negative regulators" is limited in plant genomes, the CRISPR-directed gene knockout has a restricted potential for crop improvement. Intensive application of the CRISPR/Cas system for more complicate modifications such as replacement of defect alleles by functional ones or insertion of a desired gene is required (so far reports about such modifications are very rare in crops). In addition, to provide a basis for broad practical application of CRISPR/Cas-based genome editing, more cultivars of crop species should be involved in ongoing studies. Just a few genotypes of crop species have been used for gene modifications thus far. Nevertheless, in spite of the restrictions mentioned, essential success has been achieved over a short period (3.5 years since the first publications on CRISPR/Cas application in plants).