The light-matter interaction is one of the fundamental research fields in physics. The electron is the first discovered elementary particle that makes up matter. Therefore, the interaction between electron and light field has long been the research interest of physicists. Electrons are divided into two kinds, i.e. bounded electrons and free electrons. The quantum transition of bounded electron system is constrained by the selection rules with the discrete energy levels, while the free electron systems are not. In the last decade, the experiments of photon-induced near-field electron microscopy (PINEM) have been demonstrated. The experimental setup of PINEM is based on ultrafast electron transmission microscopy (UTEM). The thoeritcal framworks have also been developed to describe the interaction between quantum free electrons and optical fields. Within macroscopic quantum electrodynamics, the concept of photon is extended to photonic quasi-particles. Solutions of maxwell's equations in medium that satisfy certain boundary conditions are called photonic quasiparticles, such as surface plasmon polaritons, phonon polaritons, or even magnetic field. The different dispersion relations of photonic quasi-particles produce abundant phenomena in the interaction between light and matter. The underlying information about the PINEM interaction can be inferred from the electron energy loss spectrum (EELS). It has been used for implementing the near-field imaging in its infancy. By now it is capable of not only realizing time-resolved dynamic imaging, reconstructing the dispersion relation of photonics crystal and its Bloch mode, but also measuring the mode lifetime directly. The PINEM has also been used to study free electron wavepacket reshaping, free electron comb, free electron attosecond pulse train, etc. Recently, this field has entered into the era of quantum optics, and people use PINEM to study novel phenomena in quantum optics, such as entanglement between free electrons and cavity photons, entanglement between free electrons and free electrons, free electron qubits, and preparation of novel light quantum states. In this paper, the theoretical and experimental development of free-electron quantum physics are reviewed. We have disscussed the application scenarios of quantum free electron system. The current difficulties and future development are envisaged.