The CRISPR/Cas system is one of the most promising 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 the 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 was carried out using the keyword CRISPR with a crop name within article titles, abstracts and keywords in the Scopus database for 45 crops. Among the 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 generate transgene-free modified plants was widely demonstrated. However, in most cases the research was aimed at approbating the technology or elucidating the function of the target gene, while the modification of just 37 target genes was related to crop improvement. We present here a catalog of these genes. In most of these cases, the modifications resulted in knockout of the genes, such as negative growth and development regulators or negative regulatiors of plant resistance. In most cases, the phenotype of the modified plants was assessed and the presence of the 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 complicated 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 the ongoing studies. Just a few genotypes of crop species have been used for gene modifications thus far. Nevertheless, in spite of the restrictions mentioned, success has been achieved over a short period (3.5 years since the first publications on the CRISPR/Cas application in plants).