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This is a review on theoretical and experimental studies on dielectric microcavities, which play a significant role in fundamental and applied research. The basic concepts and theories are introduced. Experimental techniques for fabrication of microcavities and optical characterization are described. Starting from undeformed cavities, the review moves on to weak deformation, intermediate deformation with mixed phase space, and then strong deformation with full ray chaos. Non-Hermitian physics such as avoided resonance crossings and exceptional points are covered along with various dynamical tunneling phenomena. Some specific topics such as unidirectional output, beam shifts, wavelength-scale microcavities, and rotating microcavities are discussed. The open microdisk and microsphere cavities are ideal model systems for the studies on wave chaos and non-Hermitian physics.