Compelling evidence suggests that the Standard Model falls short as a complete theory. Recent experiments have unveiled intriguing deviations from the Standard Model, underscoring the pivotal role of the nuclear precision frontier in our pursuit of physics beyond the Standard Model (BSM). This frontier is centered on meticulously measuring nuclear phenomena, thus demanding advanced theoretical predictions. This presentation will spotlight three BSM searches from three distinct physics sub-fields, all of which can be effectively tackled through nuclear experiments. In Astronomy, we will explore dark matter direct detection with nuclear detectors. In particle physics, we will delve into the quest for charged lepton flavor violation via muon-to-electron conversion. Lastly, in nuclear physics, we will investigate exotic nuclear weak interactions, utilizing beta-decays. For each inquiry, I will elucidate the open question and its origins, demonstrate how it can be approached through low-energy nuclei experiments, highlight key theoretical gaps essential for interpreting these experiments, and present cutting-edge theory developments to address these gaps. Additionally, for the latter search, I will showcase recent discoveries stemming from new measurements and theory, illustrate how novel theoretical frameworks lead to innovative measurement techniques, and present preliminary calculations for upcoming state-of-the-art experiments.