The advent of high-power ultra-short laser pulses opens up new frontiers of relativistic non-linear optics, high energy density physics and laboratory astrophysics. As the laser electric field in the particle rest frame approaches the Schwinger field $$E_{cr} = 1.3 \times 10^{18}\,\textrm{V} \textrm{m}^{-1}$$
E
cr
=
1.3
×
10
18
V
m
-
1
, the laser interaction with matter enters into the quantum electrodynamics (QED) dominated regime, where extremely rich non-linear phenomena take place, such as a violent acceleration of charged particles, copious lepton pair production, and ultra-brilliant X/$$\gamma$$
γ
-ray emission. Among them, X/$$\gamma$$
γ
-ray emission based on the laser-plasma is generally characterized by large photon flux, high brilliance, small source size, and high photon energy, which can even annihilate into lepton pairs by colliding with photons. Though various schemes have been proposed for bright high-energy photon emission and lepton generation and acceleration, many predictions remain to be confirmed and thoroughly tested in experiments. In this review, we introduce recent advances in bright X/$$\gamma$$
γ
-ray radiation and lepton pair generation in the QED regime by the interaction of relativistic intense lasers with various plasma targets. The characteristics of the radiation and secondary particles generated via these schemes are summarized, and the experimental progresses are elaborated.