Potato is an important crop due to its nutritional value and high yield potential. Improving the quality and quantity of tubers remains one of the most important breeding objectives. Genetic mapping helps to identify suitable markers for use in the molecular breeding, and combined with transgenic approaches provides an efficient way for gaining desirable traits. The advanced plant breeding tools and molecular techniques, e.g., TALENS, CRISPR-Cas9, RNAi, and cisgenesis, have been successfully used to improve the yield and nutritional value of potatoes in an increasing world population scenario. The emerging methods like genome editing tools can avoid incorporating transgene to keep the food more secure. Multiple success cases have been documented in genome editing literature. Recent advances in potato breeding and transgenic approaches to improve tuber quality and quantity have been summarized in this review.