The advent of high-power ultra-short ultra-intense laser pulses opens up the new frontiers of relativistic nonlinear optics, high-field physics, laser-driven inertial confined fusion, etc. In recent years, with the construction of high power laser facilities at a multi-petawatt (PW) level and above, the interaction between laser and matter enters into a new realm of high field physics, where extremely rich nonlinear physics is involved. In addition to classical nonlinear physics involving wave-particle interactions, relativistic effects, and ponderomotive force effects, the quantum electrodynamic (QED) effects occur, such as radiation reaction force, electron-positron pair production, strong γ-ray radiation, QED cascades, and vacuum polarization. This paper presents a brief overview of electron-positron pair creation and bright γ-ray emission driven by the extremely intense laser fields.