In this talk, I will start with a brief review on lepton-number violation (LNV) and lepton-flavor violation (LFV) in the Standard Model and beyond as well as the connection between LNV and LFV. Then, I discuss a complete family of models where lepton number is violated but the generated Majorana neutrino masses are tiny, even if the new-physics scale is below 1~TeV. The phenomenology of these models are explored, including charged-lepton flavor-violating phenomena and baryon-number-violating phenomena. I will identity scenarios where the allowed rates for $\mu^-\to e^+$-conversion in nuclei are potentially accessible to next-generation experiments.