Photonic transverse spatial mode includes two degrees of freedom, i.e., azimuthal modes and radial modes, either of which can be exploited to construct a high-dimensional Hilbert space. In the past two decades, azimuthal modes such as photonic orbital angular momentum have been deeply studied, and widely used in the fields of classical optics and quantum information. However, the research on the radial modes is still lacking at present, and it is still in the exploratory stage, so the quantum number of the radial mode is once called “a forgotten quantum number”. Recent years have witnessed a growing research interest in photonic radial modes because of their unique characteristics in light field. The preparation, measurement and manipulation methods of high-order radial modes are introducted systematically, especially the quantum entanglement correlation characteristics of photonic radial modes and the research progresses of their applications in the detection of the fundamental issues in quantum mechanics and the processing of high-dimensional quantum information.