Most of the polymers used as biomaterials for scaffolds are naturally occurring, synthetic biodegradable, and synthetic non-biodegradable polymers. Since synthetic polymers can be adapted for obtaining singular desired characteristics by applying various fabrication techniques, their use has increased in the biomedical field, in dentistry in particular. The manufacturing methods of these new structures include many processes, such as electrospinning, 3D printing, or the use of computer-aided design/computer-aided manufacturing (CAD/CAM). Synthetic polymers show several drawbacks that can limit their use in clinical applications, such as the lack of cellular recognition, biodegradability, and biocompatibility. Moreover, concerning biodegradable polymers, the time for matrix resorption is not predictable, and non-resorbable matrices are preferred for soft tissue augmentation in the oral cavity. This review aimed to determine a new biomaterial to offset the present shortcomings in the oral environment. Researchers have recently proposed a novel non-resorbable composite membrane manufactured via electrospinning that has allowed obtaining remarkable in vivo outcomes concerning angiogenesis and immunomodulation throughout the polarization of macrophages. A prototype of the protocol for in vitro and in vivo experimentation with hydrogels is explained in order to encourage innovation into the development of promising biomaterials for soft tissue augmentation in the near future.