Light-matter interactions can be mainly described by transitions of electrons, accompanied by emission, absorption, or scattering of photons. Light absorption and emission of atoms, molecules, solids and other substances play a vital role in the development of science and technology.Because of its excellent monochromaticity, directivity and coherence, laser has become a powerful tool to detect the structure and properties of matter.With the development of laser technology, the peak power of the laser pulse reaches the order of 10¹⁵ W and the laser pulse durations decrease to a few femtoseconds. Advanced optical technology makes it possible to carry out experiments at an unprecedented intensity. When the electric field intensity of laser pulse reaches or even exceeds the electric field intensity of the Coulomb potential inside the substances, the concept that the laser field is regarded as a perturbation to the motion of electrons under the constraints of the Coulomb field is no longer applicable, accompanied by a series of highly nonlinear complex dynamic processes, such as multi-photon and above threshold ionization, tunneling ionization,nonsequential double ionization and High Harmonic Generation (HHG). In this context, the emergence of ultrashort and ultra-intense pulses gradually opened up the research of strong field physics. When a macroscopic system is exposed to intense laser fields whose forces are comparable to the binding forces of valence electrons, the system will emit coherent radiation with frequencies many times that of the driving laser field. This non-perturbativeand extremely nonlinear optical phenomenon is calledhigh-order harmonic generation, whichhas become a research direction of great concern in the field of strong field physicsas a Potential Extreme Ultraviolet (EUV) source and a possible means of real-time detection of ultrafast dynamics inside matter. In the past 30 years, HHG from gases has been developed greatly based on the physical image of the three-step model, which has laid a solid foundation for attosecond physics. HHG from solids provides a new way to miniaturize devices as a EUV light source and explore the electronic structure of condensed matter system. Meanwhile, in order to find more integrated and compact EUV light source, people gradually turn their attention to solid target.Experimental observation of non-perturbative transmitted high-order harmonics generated from ZnO crystal suggested that the solid-state HHG process can be illustrated neither by conventional perturbative nonlinear optics nor by the kinematics of strong-field re-scattering.More researches demonstrated that solid-state HHG can be achieved through a wide variety of interaction media with suitable laser wavelengths from the near-infrared to terahertz range.High harmonic generation from solid materials driven by an ultrafast strong laser is a fast developing direction in interdisciplinary fields of condensed matter physics, materials science, optics and photonics. So far, the target of solid-state HHG study has been expanded from bulk metals, semiconductors, insulators to low-dimensional nanostructures. Moreover, nonperturbative harmonic signals have been successfully detected in topological insulators and from topological surface states. Compared to gaseous atoms and molecules, solid materials have higher atomic density, and the mechanism of solid-state HHG is more complicated, thus solid-state HHG possesses good application prospects in achieving new light sources, exploring physical properties as well as characterizing microscopic dynamics of materials. This article mainly reviews the experimental and theoretical progresses of solid-state HHG in recent years, and also summarizes its mechanisms and potential applications.