Any materials at temperatures higher than absolute zero emit electromagnetic waves due to the thermal fluctuations of free charges or ions. When two or more bodies at different temperatures are brought sufficiently close to each other with vacuum gap spacing smaller than the characteristic thermal wavelength, near-field radiative heat flux can exceed the far-field blackbody limit, governed by the well-known Stefan-Boltzmann law, by orders of magnitude. This article reviews the recent progress on both theoretical and experimental studies of near-field thermal radiation with an emphasis on its potential applications. Recent theoretical developments are presented, such as near-field radiation of general anisotropic materials and 2D materials, application condition of effective medium theory, and exact numerical methods for dealing with arbitrary particles or periodic nanostructures. Recent experimental achievements are also discussed, focusing on tip-plane and plane-plane configurations with various materials. The wide applications of near-field radiation are summarized in terms of thermal imaging, energy harvesting, and contactless thermal management such as modulation, rectification, and amplification. An outlook is provided on the promise of near-field thermal radiation in energy harvesting, novel thermal sources, and sensing, as well as the development of related fields such as reducing Casimir stiction, minimizing noise current, and increasing spontaneous emission rate. Challenges are also discussed, such as developing exact and fast computational techniques for complex metamaterials, understanding near-field radiation at extreme gap spacing, overcoming weak mode coupling in thermophotovoltaic (TPV) systems, measuring large-area plane-plane configuration at small gap spacing, and realizing devices based on near-field radiation.