Some basic properties of nonradiating systems are considered. A simple connection is established between the existence of residual electromagnetic potentials and the current density spectrum of the system. The properties of specific configurations based on toroidal and supertoroidal currents are modeled with the finite-difference time-domain method. Possible applications are discussed. A design of a new type of nonradiating system, based on a left-handed metamaterial is proposed and the system performance is modeled numerically.