Three-dimensional (3D) printing technology allows the production of an individualized 3D object based on a material of choice, a specific computer-aided design and precise manufacturing. Developments in digital technology, smart biomaterials and advanced cell culturing, combined with 3D printing, provide promising grounds for patient-tailored treatments. In dentistry, the “digital workflow” comprising intraoral scanning for data acquisition, object design and 3D printing, is already in use for manufacturing of surgical guides, dental models and reconstructions. 3D printing, however, remains un-investigated for oral mucosa/gingiva. This scoping literature review provides an overview of the 3D printing technology and its applications in regenerative medicine to then describe 3D printing in dentistry for the production of surgical guides, educational models and the biological reconstructions of periodontal tissues from laboratory to a clinical case. The biomaterials suitable for oral soft tissues printing are outlined. The current treatments and their limitations for oral soft tissue regeneration are presented, including “off the shelf” products and the blood concentrate (PRF). Finally, tissue engineered gingival equivalents are described as the basis for future 3D-printed oral soft tissue constructs. The existing knowledge exploring different approaches could be applied to produce patient-tailored 3D-printed oral soft tissue graft with an appropriate inner architecture and outer shape, leading to a functional as well as aesthetically satisfying outcome.