With the advent of ultra-short ultra-intense laser pulses, the interaction between light and matter enters the nonlinear physics regime dominated by radiation damping and quantum electrodynamics (QED) effects. The strong-field QED effects contain a wealth of physical processes, including radiation damping effect, high-energy gamma radiation, electron-positron pairs generation, QED cascade, vacuum polarization, and so on. These effects are frontiers and hot topics in high energy density physics and strong field physics. Among them, QED cascade is an important mechanism, which can explain the formation of the ultra-dense radiation in the cosmos and the gamma-ray burst, and the resulting dense positron source has important application prospects in high-energy physics, nondestructive assay of materials, and cancer diagnosis. In this paper, the cascading process of QED and the theoretical model are introduced, then the QED cascade development in solid targets and the resulting nonlinear physical effects are discussed. Finally, the main research results of dense positron generation in solid targets are reviewed.