Platelet concentrates for surgical use are innovative tools of regenerative medicine, and were widely tested in oral and maxillofacial surgery. Unfortunately, the literature on the topic is contradictory and the published data are difficult to sort and interpret. In periodontology and dentoalveolar surgery, the literature is particularly dense about the use of the various forms of Platelet-Rich Plasma (PRP) - Pure Platelet-Rich Plasma (P-PRP) or Leukocyte-and Platelet-Rich Plasma (L-PRP) - but still limited about Platelet-Rich Fibrin (PRF) subfamilies. In this first article, we describe and discuss the current published knowledge about the use of PRP and PRF during tooth avulsion or extraction, mucogingival surgery, Guided Tissue Regeneration (GTR) or bone filling of periodontal intrabony defects, and regeneration of alveolar ridges using Guided Bone Regeneration (GBR), in a comprehensive way and in order to avoid the traps of a confusing literature and to highlight the underlying universal mechanisms of these products. Finally, we particularly insist on the perspectives in this field, through the description and illustration of the systematic use of L-PRF (Leukocyte-and Platelet-Rich Fibrin) clots and membranes during tooth avulsion, cyst exeresis or the treatment of gingival recessions by root coverage. The use of L-PRF also allowed to define new therapeutic principles: NTR (Natural Tissue Regeneration) for the treatment of periodontal intrabony lesions and Natural Bone Regeneration (NBR) for the reconstruction of the alveolar ridges. In periodontology, this field of research will soon find his golden age by the development of user-friendly platelet concentrate procedures, and the definition of new efficient concepts and clinical protocols.