Two-dimensional (2D) materials are being actively researched due to their exotic electronic and optical properties, including a layer-dependent bandgap, a strong exciton binding energy, and a direct optical access to electron valley index in momentum space. Recently, it was discovered that 2D materials with bandgaps could host quantum emitters with exceptional brightness, spectral tunability, and, in some cases, also spin properties. This review considers the recent progress in the experimental and theoretical understanding of these localized defect-like emitters in a variety of 2D materials as well as the future advantages and challenges on the path toward practical applications.