With the continuous development of technology, the laser power has exceeded 10 PW. The interaction between such intense laser pulse and matter enters the near quantum electrodynamics (QED) regime. From the non-relativistic laser pulse, relativistic one, to ultra-relativistic one, the coupling of light field and matter can produce X/γ-rays with the photon energy from keV, MeV to even GeV. These radiation sources have the characteristics of large flux, high brilliance, high energy and short duration, which have a wide range of application prospects in material science, imaging, and medicine fields and fundamental researches in nuclear physics, high-energy-density physics and astrophysics. In this review, we systematically introduce the recent advances in X/γ-ray generation through the interaction of relativistic high intensity laser with gas, near-critical-density plasma and solid targets via synchrotron radiation, betatron radiation, betatron-like radiation, Thomson scattering and nonlinear Compton scattering. The characteristics and potential applications of high energy X/γ-ray from various schemes are also summarized, which provide theoretical reference for the future experimental researches based on laser facilities.