Understanding the nanoscale electrodynamic properties of a material at microwave frequencies is of great interest for materials science, condensed matter physics, device engineering, and biology. With specialized probes, sensitive detection electronics, and improved scanning platforms, microwave microscopy has become an important tool for cutting-edge materials research in the past decade. In this article, we review the basic components and data interpretation of microwave imaging and its broad range of applications. In addition to the general-purpose mapping of permittivity and conductivity, microwave microscopy is now exploited to perform quantitative measurements on semiconductor devices, photosensitive materials, ferroelectric domains and domain walls, and acoustic-wave systems. Implementation of the technique in low-temperature and high-magnetic-field chambers has also led to major discoveries in quantum materials with strong correlation and topological order. We conclude the review with an outlook of the ultimate resolution, operation frequency, and future industrial and academic applications of near-field microwave microscopy.