Rare genetic diseases reduce quality of life and can significantly shorten the lifespan. There are few effective treatment options for these diseases, and existing therapeutic strategies often represent only supportive or palliative care. Therefore, designing genetic-engineering technologies for the treatment of genetic diseases is urgently needed. Rapid advances in genetic editing technologies based on programmable nucleases and in the engineering of gene delivery systems have made it possible to conduct several dozen successful clinical trials; however, the risk of numerous side effects caused by off-target double-strand breaks limits the use of these technologies in the clinic. Development of adenine-to-inosine (A-to-I) and cytosine-to-uracil (C-to-U) RNA-editing systems based on dCas13 enables editing at the transcriptional level without double-strand breaks in DNA. In this review, we discuss recent progress in the application of these technologies in in vitro and in vivo experiments. The main strategies for improving RNA-editing tools by increasing their efficiency and specificity are described as well. These data allow us to outline the prospects of base-editing systems for clinical application.