A new general framework for characterizing scalar and electromagnetic (EM) nonradiating (NR) and minimum energy (ME) sources and their fields is developed that is of interest for both radiation and source reconstruction problems. NR sources are characterized in connection with the concept of reciprocity as nonreceptors. Localized ME sources are shown to be free fields truncated within the source's support. A new source analysis tool is developed that is based on the decomposition of a source and its field into their radiating and NR components. The individual radiating and reactive energy roles of the radiating and NR parts of a source are characterized. The general theory is illustrated with a time-harmonic EM example. Index Terms-Inverse problems. I. INTRODUCTION T HIS paper characterizes, in a unifying general theoretical framework, new and old results on nonradiating (NR) and minimum energy (ME) sources [1]-[3] and their fields, with applications to source analysis and reconstruction. We present this framework in the context of the inverse source problem (ISP) in which one seeks to reconstruct an unknown source from knowledge of its radiated field outside the source's support [2], [4]-[14]. The general NR and ME source-field descriptions derived in this paper apply to any source-field system (scalar or electromagnetic (EM), time-harmonic, or transient) in an arbitrary linear medium (homogeneous or inhomogeneous) and subjected to arbitrary boundary conditions. We also investigate the unique decomposition of a source and its field into their radiating and NR parts and the associated power budget.