I will discuss contemporary issues in searches for New Physics with flavor-changing neutral current transitions in beauty and charm systems. I will also discuss a novel method to study flavor-changing neutral currents in the e+ e- ? D*0 and e+ e-???B*s transitions, tuning the energy of e+ e-- collisions to the mass of the narrow vector resonance D*0 or B*s . I will present a thorough study of both short-distance and long-distance contributions to those processes in the Standard Model and investigate possible contributions of New Physics.