Quantum dots are the most exciting representatives of nanomaterials. They are synthesized by modern methods of nanotechnology pertaining to both inorganic and organic chemistry. Quantum dots possess unique physical and chemical properties; therefore, they are used in very different fields of physics, chemistry, biology, engineering and medicine. It is not surprising that the Nobel Prize in chemistry in 2023 was given for discovery and synthesis of quantum dots. In this review, modern methods of synthesis of quantum dots, their optical properties and practical applications are analyzed. In the beginning, a short historical background of quantum dots is given. Many gifted scientists, including chemists and physicists, were engaged in these studies. The synthesis of quantum dots in solid and liquid matrices is described in detail. Quantum dots are well-known owing to their unique optical properties, that is why the attention in the review is focused on the quantum-size effect. The causes for fascinating blinking of quantum dots and techniques for observation of a single quantum dot are explained. The last part of the review describes important applications of quantum dots in biology, medicine and quantum technologies. Bibliography - 772 references.