The periodontium is a complex hierarchical structure composed of alveolar bone, periodontal ligament, cementum, and gingiva. Periodontitis is an inflammatory disease that damages and destroys the periodontal tissues supporting the tooth. Periodontal therapies aim to regenerate the lost tissues, yet current treatments lack the integration of multiple structural/biochemical instructive cues to induce a coordinated regeneration, which leads to limited clinical outcomes. Hierarchical biomaterial scaffolds offer the opportunity to recreate the organization and architecture of the periodontium with distinct compartments, providing structural biomimicry that facilitates periodontal regeneration. Various scaffolds have been fabricated and tested preclinically, showing positive regenerative results. This review provides an overview of the recent research on hierarchical scaffolds for periodontal tissue engineering (TE). First, the hierarchical structure of the periodontium is described, covering the limitations of the current treatments used for periodontal regeneration and presenting alternative therapeutic strategies, including scaffolds and biochemical factors. Recent research regarding hierarchical scaffolds is highlighted and discussed, in particular, the scaffold composition, fabrication methods, and results from in vitro/in vivo studies are summarized. Finally, current challenges associated with the application of hierarchical scaffolds for periodontal TE are debated and future research directions are proposed.