One of the most important problems in condensed matter physics involves the microscopic understanding of how localized electrons at high temperatures turn into itinerant heavy quasi-particles in a low temperature metallic state. The fundamental mechanism of this evolution lies at the heart of heavy-electron physics and depends on the Kondo coupling between the conduction electrons (CE) and the localized d or f electrons. Electron spin resonance (ESR) probes microscopically both the local moment (LM) spins and CE in different strongly correlated electron materials such as high-temperature superconductors, pnictides, heavy fermion systems. LM ESR is observed in compounds with paramagnetic ions and localized electrons. CE spin resonance (CESR) can be detected in metallic systems based on light elements exhibiting an enhanced Pauli susceptibility. We discuss here the ESR studies in several undoped Yb-, Ce-, and Eu-based intermetallics which share the nature of both, the LM-like and CESR-like ESR signals. Moreover, ESR measurements in the new ternary phosphide $YbRh_6P_4$ are reported. Different theoretical approaches which were proposed to explain the origin of such unexpected ESR behavior are discussed.
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