New physics effects in rare Z decays

Virtual effects induced by new physics in rare Z decays are reviewed. Since the expected sensitivity of the giga-Z linear collider is of the order of $10^{-8}$, we emphasize the importance of any new physics effect that gives a prediction above this limit. It is also pointed out that an improvement on the known experimental constraints on rare Z decays will provide us with a critical test of the validity of the standard model at the loop level.