Atomic filters utilize the spectroscopic features of atomic resonant transitions to achieve frequency selection, featuring prominent merits including high peak transmittance, narrow transmitted bandwidth, and superior out-of-band noise suppression. Over the past decade, birefringent atomic filters, represented by the Faraday anomalous dispersion optical filter (FADOF) and the induced-dichroism-excited atomic line filter (IDEALF), have developed rapidly, with operating wavelengths covering the visible to near-infrared regions, and have demonstrated unique application value in fields such as laser communication, lidar, and frequency-stabilized lasers. However, due to the Doppler broadening and collision broadening caused by high-speed motion and frequent collisions of thermal atoms, the transmitted bandwidth of existing thermal-atom optical filters is difficult to narrow to the order of the natural linewidth, which restricts their application in the field of ultra-narrowband filtering. The proposal of cold-atom optical filters provides a new approach to further reduce the transmitted bandwidth. By employing laser cooling techniques to slow atoms, the Doppler effect associated with atomic motion is significantly suppressed. Based on this principle, the cold-atom optical filters realized to date can be divided into two main categories according to their cooling methods and optical rotation mechanisms: FADOFs and IDEALFs based on a magneto-optical trap, and FADOFs based on diffuse laser cooling. This article details the optical rotation principles, experimental schemes, and research progress of these two types of cold-atom optical filters. compares their performance with state-of-the-art benchmarks worldwide, and analyzes their respective advantages and disadvantages.Their performance is compared with state-of-the-art results worldwide, and their respective advantages and limitations are discussed. Finally, the great potential of cold-atom optical filters for realizing active Faraday optical frequency standards, underwater optical communication, and single-photon sources is presented, which is expected to open up new avenues for the development of quantum metrology and quantum communication network technologies.