The demand for sophisticated tools and approaches in heat management and control has triggered fast development of emerging fields including conductive thermal metamaterials, nanophononics, far-field and near-field radiative thermal management, etc. In this review, we cast a unified perspective on the control of heat transfer, based on which the related studies can be considered as complementary paradigms toward manipulating physical parameters and realizing unprecedented phenomena in heat transfer using artificial structures, such as thermal conductivity in heat conduction, thermal emissivity in radiation, and properties related to multi-physical effects. The review is divided into three parts that focus on the three main categories of heat flow control, respectively. Thermal conduction and radiation are emphasized in the first and second parts at both macro-and micro-scale. The third part discusses the efforts to actively introduce heat sources or tune the material parameters with multi-physical effects in both conduction and radiation, including works using thermal convection. We conclude the review with challenges in this research topic and new possibilities about topological thermal effects, heat waves, and quantum thermal effects.