Polyphenols are a class of ubiquitous compounds distributed in nature, with fascinating inherent biocompatible, bioadhesive, antioxidant, and antibacterial properties. The unique polyphenolic structures based on catechol or pyrogallol moieties allow for strong non-covalent interactions (e.g., multiple hydrogen bonding, electrostatic, and cation-π interactions) as well as covalent interactions (e.g., Michael addition/Schiff-base reaction, radical coupling reaction, and dynamic coordination interactions with boronate or metal ions). This review article provides an overview of the polyphenol-based scaffolds including the hydrogels, films, and nanofibers that have emerged from chemical and functional signatures during the past years. A full description of the structure-function relationships in terms of their utilization in wound healing, bone regeneration, and electroactive tissue engineering is also carefully discussed, which may pave the path towards the rational design and facile preparation of next-generation polyphenol scaffolds for tissue engineering applications.