Periodontitis is a global, multifaceted, chronic inflammatory disease caused by bacterial microorganisms and an exaggerated host immune response that not only leads to the destruction of the periodontal apparatus but may also aggravate or promote the development of other systemic diseases. The periodontium is composed of four different tissues (alveolar bone, cementum, gingiva, and periodontal ligament) and various non-surgical and surgical therapies have been used to restore its normal function. However, due to the etiology of the disease and the heterogeneous nature of the periodontium components, complete regeneration is still a challenge. In this context, guided tissue/bone regeneration strategies in the field of tissue engineering and regenerative medicine have gained more and more interest, having as a goal the complete restoration of the periodontium and its functions. In particular, the use of electrospun nanofibrous scaffolds has emerged as an effective strategy to achieve this goal due to their ability to mimic the extracellular matrix and simultaneously exert antimicrobial, anti-inflammatory and regenerative activities. This review provides an overview of periodontal regeneration using electrospun membranes, highlighting the use of these nanofibrous scaffolds as delivery systems for bioactive molecules and drugs and their functionalization to promote periodontal regeneration.