Innovation in the healthcare profession to solve complex human problems has always been emulated and based on solutions proven by nature. The conception of different biomimetic materials has allowed for extensive research that spans several fields, including biomechanics, material sciences, and microbiology. Due to the atypical characteristics of these biomaterials, dentistry can benefit from these applications in tissue engineering, regeneration, and replacement. This review highlights an overview of the application of different biomimetic biomaterials in dentistry and discusses the key biomaterials (hydroxyapatite, collagen, polymers) and biomimetic approaches (3D scaffolds, guided bone and tissue regeneration, bioadhesive gels) that have been researched to treat periodontal and peri-implant diseases in both natural dentition and dental implants. Following this, we focus on the recent novel application of mussel adhesive proteins (MAPs) and their appealing adhesive properties, in addition to their key chemical and structural properties that relate to the engineering, regeneration, and replacement of important anatomical structures in the periodontium, such as the periodontal ligament (PDL). We also outline the potential challenges in employing MAPs as a biomimetic biomaterial in dentistry based on the current evidence in the literature. This provides insight into the possible increased functional longevity of natural dentition that can be translated to implant dentistry in the near future. These strategies, paired with 3D printing and its clinical application in natural dentition and implant dentistry, develop the potential of a biomimetic approach to overcoming clinical problems in dentistry.