Single-photon detectors enable the detection of extremely weak light with remarkable temporal precision. This capability provides crucial technological support for precise distance measurements and high-resolution imaging under low-light conditions. Silicon and silicon-based germanium single-photon detectors can operate in a wide spectrum from the visible to the near-infrared region, and exhibit fundamental advantages without needing heterogeneous integration. In recent years, there has been continuous progress in the miniaturization of silicon-based single-photon diodes and corresponding read-out circuits. The integration scheme of 3D stacking has enabled the optimization of the devices and circuits at different process nodes. This evolution has comprehensively enhanced system volumes and performances. Thus, detection systems and applications of silicon-based single-photon technology continue to expand. In this paper, we review the structural evolution, performance characterization, manufacturing processes, and analog front-end circuits of single-photon detectors based on CMOS/CIS technology and silicon-based germanium avalanche photodiodes. Additionally, we provide an overview of the critical circuits in typical application scenarios.