Potato may have anthocyanin-colored tuber skin, tuber flesh, flowers, leaves, stems and eyes. Anthocyanins protect photosynthetic apparatus of plant cell, scavenge free radicals under stress conditions, increase efficiency of phosphorus and nitrogen uptake, possess osmoregulatory function, antimicrobial activity and have a number of other useful properties. Anthocyanins are also known for their health benefit: diabetes type II and cardiovascular diseases protection, anti-inflammatory effect, etc. Thus, anthocyanins are important for adaptation of plants to unfavorable environment conditions as well as for nutritional value when they are taken with food. Since potato Solanum tuberosum L. is one of the main crop species, possibility to increase anthocyanin content in tuber flesh is important. Anthocyanin concentration in pigmented tuber flesh is similar to that in blueberries, blackberries, cranberries and red grapes. It is important that cooking as well as long storage of potato tubers doesn't affect anthocyanin content. Coloration traits (red or purple tuber flesh) are included in ongoing breeding programs. Therefore, development of tools (convenient diagnostic PCR-markers for anthocyanin biosynthesis genes) for accelerated and efficient selection is of importance. The goal of the current review is to summarize information on the genes regulating anthocyanin biosynthesis in potato and assess possibility of development of diagnostic marker for prediction of tuber flesh color before tuber formation. Anthocyanin biosynthesis takes place in cytosol with the help of enzymes CHS, CHI, DFR, F3H, F3′H, F3′5′H and ANS, after that anthocyanins are transported to vacuoles. Activation of biosynthesis is controlled by MBW complex consisting of transcription factors MYB, bHLH and WD40. This complex activates transcription of structural genes encoding the enzymes mentioned above. A number of MYB-encoding genes are identified in potato, among them StAN1 related with anthocyanin biosynthesis. This gene corresponds to the D locus previously revealed with genetic dissection approach and mapped to chromosome 10. The genes encoding bHLH (StJAF13 and StbHLH1) and WD40 (StWD40) have been revealed only by their homology with similar genes of other plant species, but not by genetic dissection, probably because they have no allelic diversity. Thus, the main gene determining high variability of potato by the coloration traits is StAN1. Its allelic variants are described and shown to be related with anthocyanin synthesis efficiency. The StAN1 alleles can be easily distinguished by PCR fragments lengths, what allows constructing convenient diagnostic markers for selection. In some cases, the lack of anthocyanins is due to mutation of a structural gene. This was described in the literature for the R locus encoding DFR enzyme. Mutation of other structural gene, StF3′5′H (locus P), just partially disrupts anthocyanin synthesis, not effecting red pigments, but blue and purple only. This makes the StF3′5′H an attractive target for marker-assisted identification of genotypes with different tuber flesh color - purple or red. Thus, there are two main targets for breeding anthocyanin-colored potato - StAN1 and StF3′5′H.