The present paper reviews the recent efforts and achievements regarding the fabrication techniques of self-assembled quantum dot pairs. Quantum dot pairs, the simplest but most-investigated quantum dot molecules, have attracted significant attention due to their potential applications in quantum information technologies. Coupled quantum dot pairs have been used to implement quantum qubits, quantum gates, and exciton-spin memory. In the last several decades, the development of epitaxial growth has advanced the design and control of how novel quantum dot pairs form at nanoscale. Both vertically and laterally aligned quantum dot pairs can be grown using the molecular beam epitaxy technique. In this review, we provide assess various growth methods of aligned quantum dot pairs fabricated by molecular beam epitaxy. We highlight the recent development of novel growth techniques and discuss the morphological, electrical, and optical properties of quantum dot pairs. Using advanced epitaxial growth techniques to fabricate well-controlled quantum dot pairs opens the door to developing of advanced quantum information technologies and understanding the unveiled physics and properties of artificial quantum molecules.