Introducing targeted changes in the genome of living cells or whole organisms makes it possible to solve many problems of basic science, biotechnology, and medicine. Target gene knockout in zygotes helps to study the functions of the gene in the corresponding organisms, while replacement of single nucleotide in DNA provides an opportunity to correct gene mutations and to treat hereditary disorders. Adding a gene into a proper genome region can be used to construct producer cells or organisms with certain properties. Such genomic manipulations are possible due to the technology known as genome editing. In this technology, a break is introduced into a certain chromosomal DNA region with an endonuclease recognizing a unique sequence, and DNA integrity is then restored by cell repair systems. Custom-designed endonucleases able to cleave a selected target sequence are necessary tools for genome editing. Programmable endonucleases of a new type were constructed on the basis of bacterial transcription activator-like (TAL) effectors (TALEs), marking an important step in the development of genome editing and promoting its broad application. The review considers the history of discovering TALEs and creating TALE nucleases and describes their advantages over zinc finger endonucleases, which were constructed earlier. A section focuses on the genetic modifications that can be performed using various genome editing techniques.