Interfacial thermal resistance (ITR) is the main obstacle for heat flows from one material to another. Understanding ITR becomes essential for the removal of redundant heat from fast and powerful electronic and photonic devices, batteries, etc. In this review, a comprehensive examination of ITR is conducted. Particular focus is placed on the theoretical, computational, and experimental developments in the 30 years after the last review given by Swartz and Pohl in 1989. To be self-consistent, the fundamental theories, such as the acoustic mismatch model, the diffuse mismatch model, and the two-temperature model, are reviewed. The most popular computational methods, including lattice dynamics, molecular dynamics, the Green’s function method, and the Boltzmann transport equation method, are discussed in detail. Various experimental tools in probing ITR, such as the time-domain thermoreflectance, the thermal bridge method, the $3\omega$ method, and the electron-beam self-heating method, are illustrated. This review covers ITR (also known as the thermal boundary resistance or Kapitza resistance) of solid-solid, solid-liquid, and solid-gas interfaces. Such fundamental challenges as how to define the interface, temperature, etc. when the materials scale down to the nanoscale or atomic scale and the opportunities for future studies are also pointed out.