This article reintroduces and reinforces our proposed paradigm that involves specific individual “dual-purpose” radionuclides or radionuclide pairs with emissions suitable for both imaging and therapy and which, when molecularly (selectively) targeted using appropriate carriers, would allow pretherapy low-dose imaging as well as higher-dose therapy in the same patient. We have made an attempt to sort out and organize a number of such theragnostic radionuclides and radionuclide pairs that may thus potentially bring us closer to the age-long dream of personalized medicine for performing tailored low-dose molecular imaging (single-photon emission computed tomography/computed tomography or positron emission tomography/CT) to provide the necessary pretherapy information on biodistribution,... dosimetry, the limiting or critical organ or tissue, the maximum tolerated dose, and so forth, followed by performing higher-dose targeted molecular therapy in the same patient with the same radiopharmaceutical. Beginning in the 1980s, our work at Brookhaven National Laboratory with such a “dual-purpose” radionuclide, tin-117m, convinced us that it is arguably one of the most promising theragnostic radionuclides, and we have continued to concentrate on this effort. Our results with this radionuclide are therefore covered in somewhat greater detail in this publication. A major problem that continues to be addressed, but remains yet to be fully resolved, is the lack of availability, in sufficient quantities, of a majority of the best candidate theragnostic radionuclides in a no-carrier-added form. A brief description of the recently developed new or modified methods at Brookhaven National Laboratory for the production of 5 theragnostic radionuclide/radionuclide pair items, whose nuclear, physical, and chemical characteristics seem to show great promise for personalized cancer and other therapies, is provided.