Genome editing is a powerful tool that allows study of the properties of genes or changes to be made to the genetic sequence. Programmable nucleases that can induce double-strand breaks in the genomic sequence of interest have been developed over the past few decades. After initiation of a double-strand break (DSB) in DNA, the DSB can be repaired by the NHEJ (non-homologous end joining), which leads to various errors and gene knockout. Other repair options, HDR (homology directed repair) or SSTR (single-strand template repair), allow researchers to make desired changes in the gene. HDR occurs in the presence of a donor template, in natural conditions the donor template is a sister chromatid. The efficiency of HDR and SSTR is significantly lower than the efficiency of NHEJ in genome editing. Double-stranded, single-stranded and long single-stranded DNAs are used to increase efficiency and to make desired changes in genomic DNA. In this review, we discuss donor molecules that are used for DSB repair using HDR or SSTR during genome editing, their application, and modifications to increase the efficiency of HDR and SSTR.