Fruit and berry crops, as well as grapes, are important parts of the human diet and, at the same time, significant objects of genetic, breeding, biochemical and nutritional research. Traditional approaches of crop research and improvement are now complemented by effective modern genetic technologies. In this review, we analyze and summarize the achievements in genome editing of fruit, berry crops and grapes. New approaches accelerate the improvement of genotypes for many groups of traits: plant resistance to unfavorable environmental factors, flowering and ripening time, plant architectonics, fruit shelf time and biochemical composition. Genome editing using the CRISPR/Cas9 system has been successfully tested on the most important vegetatively propagated fruit and berry crops (apple, pear, orange, kumquat, grapefruit, banana, strawberry and kiwi) and grapes. About 30 genes of these crops have been used as targets for the introduction of desired mutations using the CRISPR/Cas9 system. The most valuable results are the improvement of important agronomic traits. For 24 genes it has been shown that their knockout can result in the improvement of varieties. In addition, the review pays attention to the comparative analysis of the explant types of vegetatively propagated crops used for the delivery of editing genetic constructs, as well as the comparison of the editing efficiency depending on the variation of the objects used, delivery methods, etc. The article discusses the existing limitations that need to be overcome for a wider application of genomic editing in order to improve varieties of fruit and berry crops, as well as grapes.