Terahertz metamaterial absorber has the advantages of strong absorption, thin thickness and light weight, and has been widely used in stealth materials, frequency selective surfaces, terahertz imaging, communication sensing, and so on. However, as for the traditional terahertz metamaterial absorbers based on metal-patch, once they are processed, their absorption performance will be unchangeable. To solve this problem, researchers have designed tunable terahertz absorbers by adding active metamaterials. Combined with the research status of tunable terahertz metamaterial absorbers at home and abroad, this paper classifies and expounds several typical of tunable terahertz metamaterial absorbers, focusing on the research work of single-band, multi-band, broadband, and switchable dual-function terahertz metamaterial absorbers, and finally analyzes their future development trends.