Tannins are one of the most natural, non-toxic, and highly reactive aromatic biomolecules classified as polyphenols. The reactive phenolic compounds present in their chemical structure can be an alternative precursor for the preparation of several polymeric materials for applications in distinct industries: adhesives and coatings, leather tanning, wood protection, wine manufacture, animal feed industries, and recently also in the production of new porous materials (i.e., foams and gels). Among these new polymeric materials synthesized with tannins, organic and carbon gels have shown remarkable textural and physicochemical properties. Thus, this review presents and discusses the available studies on organic and carbon gels produced from tannin feedstock and how their properties are related to the different operating conditions, hence causing their cross-linking reaction mechanisms. Moreover, the steps during tannin gels preparation, such as the gelation and curing processes (under normal or hydrothermal conditions), solvent extraction, and gel drying approaches (i.e., supercritical, subcritical, and freeze-drying) as well as the methods available for their carbonization (i.e., pyrolysis and activation) are presented and discussed. Findings from organic and carbon tannin gels features demonstrate that their physicochemical and textural properties can vary greatly depending on the synthesis parameters, drying conditions, and carbonization methods. Research is still ongoing on the improvement of tannin gels synthesis and properties, but the review evaluates the application of these highly porous materials in multidisciplinary areas of science and engineering, including thermal insulation, contaminant sorption in drinking water and wastewater, and electrochemistry. Finally, the substitution of phenolic materials (i.e., phenol and resorcinol) by tannin in the production of gels could be beneficial to both the bioeconomy and the environment due to its low-cost, bio-based, non-toxic, and non-carcinogenic characteristics.