Molecular beam epitaxy (MBE), a workhorse of the semiconductor industry, has progressed rapidly in the last few decades in the development of novel materials. Recent developments in condensed matter and materials physics have seen the rise of many novel quantum materials that require ultra-clean and high-quality samples for fundamental studies and applications. Novel oxide-based quantum materials synthesized using MBE have advanced the development of the field and materials. In this review, we discuss the recent progress in new MBE techniques that have enabled synthesis of complex oxides that exhibit "quantum" phenomena, including superconductivity and topological electronic states. We show how these techniques have produced breakthroughs in the synthesis of 4d and 5d oxide films and heterostructures that are of particular interest as quantum materials. These new techniques in MBE offer a bright future for the synthesis of ultra-high quality oxide quantum materials.