We derive a new description of two complementary classes of scalar, vector, or tensor sources, namely, nonradiating (NR) sources and sources that lack a NR part, ie,“purely radiating” sources. The class of purely radiating sources is shown to be exactly the class of solutions—within the source's support—of the homogeneous form of the associated partial differential equation relating the sources to their fields; ie, purely radiating sources are themselves fields. We show that this result is related to the well-known reciprocity principle and establish a new definition of a localized NR source based on that principle. A broad class of physically relevant sources, all of which possess a NR part, is identified. The role of NR sources in absorption of radiation and energy storage is addressed.