Mutation is a source of genetic diversity widely used in breeding programs for the acquisition of agronomically interesting characters in commercial varieties of the Prunus species, as well as in the rest of crop species. Mutation can occur in nature at a very low frequency or can be induced artificially. Spontaneous or bud sport mutations in somatic cells can be vegetatively propagated to get an individual with the mutant phenotype. Unlike animals, plants have unlimited growth and totipotent cells that let somatic mutations to be transmitted to the progeny. On the other hand, in vitro tissue culture makes it possible to induce mutation in plant material and perform large screenings for mutant’s selection and cleaning of chimeras. Finally, targeted mutagenesis has been boosted by the application of CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats)/Cas9 and Transcription activator-like effector nuclease (TALEN) editing technologies. Over the last few decades, environmental stressors such as global warming have been threatening the supply of global demand for food based on population growth in the near future. For this purpose, the release of new varieties adapted to such changes is a requisite, and selected or generated Prunus mutants by properly regulated mechanisms could be helpful to this task. In this work, we reviewed the most relevant mutations for breeding traits in Prunus species such as flowering time, self-compatibility, fruit quality, and disease tolerance, including new molecular perspectives in the present postgenomic era including CRISPR/Cas9 and TALEN editing technologies.