While shielding in collisional plasmas obeys the standard Debye result, shielding in collisionless plasmas is far more complex than commonly believed. For example, a one-dimensional (highly magnetized), immobile-ion plasma can, in some circumstances, anti-shield a positive test charge; i.e. the plasma becomes more positive in the vicinity of the test charge. When shielding does occur, it results from electrons dynamically trapped in the neighborhood of the test charge. A new theory of collisionless (Dynamic) shielding in one, two and three dimensions is presented here, and is in excellent agreement with experiments in pure electron plasmas. Because the distribution functions found in Dynamic shielding are highly non-Maxwellian in the non-linear regime, collisionless Dynamic shielding can be substantially less efficacious than collisional Debye shielding.