Tannin-rich compounds are widely produced as by-products of many agro-industrial processes. Tannase is an attractive hydrolase for the bioconversion of tannin-rich materials into value-added products by accelerating the hydrolysis of ester and depside linkages. It has opened new opportunities in several industrial sectors, such as food, drinks, and medicines. Primary sources of tannase are microorganisms, particularly bacteria. Tannases or tannin acyl hydrolases, are an important group of biotechnologically relevant enzymes in several industrial applications. Microbial tannases are mostly induced extracellular enzymes produced by submerged and solid-state fermentation. Tannins containing low-value agro-industrial wastes are being extensively used in industries. This review provides a more in-depth knowledge of the research related to the biochemical characteristics of the tannase enzyme activity (in terms of molecular weight, the effect of pH, the effect of temperature, the effect of metal ions, inhibitor, and chelator), extraction, and purification methods. Additionally, the potential use of agricultural waste as a substrate for tannase production has also been reviewed, including the utilization of pomegranate peel waste (PmPW), banana peel waste (BPW), or potato peel waste (PtPW).