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Hyperon physics offers a distinctive laboratory for probing the intensity frontier and searching for physics beyond the Standard Model. This review summarizes recent results from the BESIII experiment, including pioneering studies of dark baryons, massless BSM particles, and invisible decay modes, together with investigations of baryon- and lepton-number violation. A central highlight is the determination of the $\Lambda$ electric dipole moment using quantum-entangled hyperon-antihyperon pairs, achieving a sensitivity three orders of magnitude beyond previous limits. These measurements provide world-leading constraints on new physics scenarios and establish a robust foundation for next-generation precision studies. By integrating experimental progress with theoretical developments and future facility prospects, this review emphasizes the critical role of hyperon probes in testing the fundamental laws of nature.
