Clean distributable energy source is expected to develop for the sustainable societies in the 21st century. Recent research development of condensed matter nuclear science (CMNS), which is the descendant new research filed of past controversial “cold fusion” saga, is now revealing the new possibility of potential clean nuclear energy in portable size devices, although the stage of research is still basic and fundamental. This review paper describes; 1) Brief experimental results of anomalous excess heat generation with 4He ash without visible neutron and gamma-ray emission by the two methods of deuterium loading into Pd-nano-metal reactor samples based on D2O electrolysis and the one method of gas-phase deuterium loading. Key issues for further engineering-phase development are discussed. 2) For the physical understanding of this “new phenomena”, as new-type of deuteron-related fusion reactions in the ordering and constraint dynamics of deuterium clustering in condensed matter as PdDx lattice or surface, brief review on the theoretical progress of condensed cluster fusion, typically 4D multi-body fusion by the tetrahedral symmetric condensate (TSC), is given with easier physical explanations. Key issues as reproducibility and increment of power density are summarized.