Computational nuclear oncology for precision radiopharmaceutical therapy (RPT) is a new frontier for theranostic treatment personalization. A key strategy relies on the possibility to incorporate clinical, biomarker, image-based, and dosimetric information in theranostic digital twins (TDTs) of patients to move beyond a one-size-fits-all approach. The TDT framework enables treatment optimization by real-time monitoring of the real-world system, simulation of different treatment scenarios, and prediction of resulting treatment outcomes, as well as facilitating collaboration and knowledge sharing among health care professionals adopting a harmonized TDT. To this aim, the major social, ethical, and regulatory challenges related to TDT implementation and adoption have been analyzed. Methods: The artificial intelligence-dosimetry working group of the Society of Nuclear Medicine and Molecular Imaging is actively proposing, motivating, and developing the field of computational nuclear oncology, a unified set of scientific principles and mathematic models that describe the hierarchy of etiologic mechanisms involved in RPT dose response. The major social, ethical, and regulatory challenges to realize TDTs have been highlighted from the literature and discussed within the working group, and possible solutions have been identified. Results: This technology demands the implementation of advanced computational tools, harmonized and standardized collection of large real-time data, and modeling protocols to enable interoperability across institutions. However, current legislations limit data sharing despite TDTs' benefiting from such data. Although anonymizing data is often sufficient, ethical concerns may prevent sharing without patient consent. Approaches such as seeking ethical approval, adopting federated learning, and following guidelines can address this issue. Accurate and updated data input is crucial for reliable TDT output. Lack of reimbursement for data processing in treatment planning and verification poses an economic barrier. Ownership of TDTs, especially in interconnected systems, requires clear contracts to allocate liability. Complex contracts may hinder TDT implementation. Robust security measures are necessary to protect against data breaches. Cross-border data sharing complicates risk management without a global framework. Conclusion: A mechanism-based TDT framework can guide the community toward personalized dosimetry-driven RPT by facilitating the information exchange necessary to identify robust prognostic or predictive dosimetry and biomarkers. Although the future is bright, we caution that care must be taken to ensure that TDT technology is implemented in a socially responsible manner.