The conduction of heat is one of the fundamental energy transport mechanisms in nature. In addition to the fundamental insights in physics, the study of heat conduction is also valuable for an array of applications, including thermal management, thermal barrier coating and thermal protection, as well as thermoelectrics. Clearly, from various technological aspects, there are quite different expectations in thermal conductivity. Within this context, we are delighted to provide a cutting-edge insight into emerging mechanisms for manipulating thermal conduction, via organizing a special topic with a selection of four Invited Reviews, two Research Articles, and two News & Views. These papers summarize the recent advances in the phonon transport theory, phononic metamaterials, and applications in thermal management and renewable energy.Recently, emerging phonon phenomena have been found. Chen and co-workers [1] summarize the state-of-the-art advances in several fascinating phonon transport phenomena, including the phonon coherence, topological properties of phonons, weak coupling of phonons, and higher-order phonon anharmonicity. Cao and co-workers [2] discuss the possibilities to realize thermal smart materials with tunable thermal conductivity as well as their applications.In nanoscale devices, with the number of interfaces increasing, the interfacial thermal resistance is becoming even more important than the channel material itself. Besides interfacial thermal resistance, an interface may influence phonon anharmonicity. Cai and co-workers [3] review the recent studies of phonon anharmonicity and thermal conductivity of twodimensional van der Waals materials. Graphene has ultrahigh thermal conductivity, which is expected to be utilized in thermal interface materials. Lin and co-workers [4] present the rational design of graphene structures for high performance thermal interface materials. Different mechanisms and design strategies to enhance interfacial thermal conductance are discussed.In the original research article, Zhang and co-workers [5] discuss phonon damping in one-dimensional lattices with asymmetric interaction potential. In the original research article, Huang and co-workers [6] discuss the efficiency limit of thermal concentrators and explore the possible strategies to break such efficiency limit by the concept of conductivity coupling.Strain inevitably exists at interfaces between dissimilar materials. Typically, strain can change lattice structure and thus physical properties. This is especially important in thermal transport at the nanoscale. In the News & Views, Zhan and coworkers [7] discuss the coupled thermal stress and heat at a small scale. In recent years, active and switchable control of thermal conductivity has attracted intensive research interest. In the News & Views, Liu and co-workers [8] introduce the active and reversible modulation in thermal conductivity of different types of solid materials.In conclusion, we would like to thank the authors for providing their important contributions...