Technetium-99m (99mTc) plays a major role in diagnostic nuclear medicine and has not yet been replaced with any other radionuclides. The 99mTc is a decay product of molybdenum-99 (99Mo) and it is available through a 99Mo/99mTc generator. The 99Mo can be produced either from the fission reaction of uranium-235 or from neutron-irradiated of natural/enriched molybdenum-98. The non-fission 99Mo/99mTc generator has a low specific activity of 99Mo. This limitation, however, can be overcome by the use of high-capacity adsorbents for 99Mo. This review is focused on the current progress and future challenges in the development of high-capacity adsorbent materials for non-fission molybdenum-99 (99Mo) in the application of 99Mo/99mTc generator. We briefly summarized some materials as well as nanomaterials that show high adsorption capacity for non-fission 99Mo. We also highlighted several synthesis methods, including the green synthesis method using plant extracts which can be potentially used to obtain high-capacity adsorbent materials.