Quantum criticality in heavy-fermion (HF) metals refers to the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. HF metals, particularly rare-earth-based intermetallic compounds, have emerged as prototypical systems to study quantum critical points (QCPs). These systems exhibit unique properties, such as non-Fermi-liquid behavior and unconventional superconductivity, which are central to understanding strongly correlated quantum matter. The article discusses several key aspects of quantum criticality in HF metals, including: 1. **Basic Issues**: The extent to which quantum criticality in HF metals goes beyond standard order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, and the interplay between quantum criticality and unconventional superconductivity. 2. **Kondo Effect**: The Kondo effect, where a localized magnetic moment couples to conduction electrons, leading to the formation of a Kondo singlet. This effect is crucial for understanding the properties of HF metals. 3. **Non-Fermi-liquid Phenomena**: The non-Fermi-liquid behavior, characterized by a linear temperature dependence of electrical resistivity, is a hallmark of quantum criticality in HF metals. 4. **Quantum Critical Scaling**: The scaling behavior at QCPs, including the divergence of the Grüneisen ratio and the effective mass, provides insights into the universality classes of quantum critical points. 5. **Fermi Surface and Energy Scales**: The collapse of the Fermi surface and the presence of multiple energy scales at QCPs are important features that distinguish quantum criticality from classical phase transitions. 6. **Superconductivity**: The relationship between quantum criticality and superconductivity, including the role of Cooper pairing mechanisms and the proximity to QCPs, is a topic of ongoing research. The article also highlights the experimental and theoretical efforts that have contributed to the understanding of quantum criticality in HF metals, emphasizing the importance of these systems in advancing the field of strongly correlated electron systems.Quantum criticality in heavy-fermion (HF) metals refers to the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. HF metals, particularly rare-earth-based intermetallic compounds, have emerged as prototypical systems to study quantum critical points (QCPs). These systems exhibit unique properties, such as non-Fermi-liquid behavior and unconventional superconductivity, which are central to understanding strongly correlated quantum matter. The article discusses several key aspects of quantum criticality in HF metals, including: 1. **Basic Issues**: The extent to which quantum criticality in HF metals goes beyond standard order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, and the interplay between quantum criticality and unconventional superconductivity. 2. **Kondo Effect**: The Kondo effect, where a localized magnetic moment couples to conduction electrons, leading to the formation of a Kondo singlet. This effect is crucial for understanding the properties of HF metals. 3. **Non-Fermi-liquid Phenomena**: The non-Fermi-liquid behavior, characterized by a linear temperature dependence of electrical resistivity, is a hallmark of quantum criticality in HF metals. 4. **Quantum Critical Scaling**: The scaling behavior at QCPs, including the divergence of the Grüneisen ratio and the effective mass, provides insights into the universality classes of quantum critical points. 5. **Fermi Surface and Energy Scales**: The collapse of the Fermi surface and the presence of multiple energy scales at QCPs are important features that distinguish quantum criticality from classical phase transitions. 6. **Superconductivity**: The relationship between quantum criticality and superconductivity, including the role of Cooper pairing mechanisms and the proximity to QCPs, is a topic of ongoing research. The article also highlights the experimental and theoretical efforts that have contributed to the understanding of quantum criticality in HF metals, emphasizing the importance of these systems in advancing the field of strongly correlated electron systems.