Low back pain is an extremely common illness syndrome that causes patient suffering and disability and requires urgent solutions to improve the quality of life of these patients. Treatment options aimed to regenerate the intervertebral disc (IVD) are still under development. The cellular complexity of IVD, and consequently its fine regulatory system, makes it a challenge to the scientific community. Biomaterials-based therapies are the most interesting solutions to date, whereby tissue engineering and regenerative medicine (TE&RM) strategies are included. By using such strategies, i.e., combining biomaterials, cells, and biomolecules, the ultimate goal of reaching a complete integration between native and neo-tissue can be achieved. Hydrogels are promising materials for restoring IVD, mainly nucleus pulposus (NP). This study presents an overview of the use of hydrogels in acellular and cellular strategies for intervertebral disc regeneration. To better understand IVD and its functioning, this study will focus on several aspects: anatomy, pathophysiology, cellular and biomolecular performance, intrinsic healing processes, and current therapies. In addition, the application of hydrogels as NP substitutes will be addressed due to their similarities to NP mechanical properties and extracellular matrix. These hydrogels can be used in cellular strategies when combined with cells from different sources, or in acellular strategies by performing the functionalization of the hydrogels with biomolecules. In addition, a brief summary of therapies based on simple injection for primary biological repair will be examined. Finally, special emphasis will focus on reviewing original studies reporting on the use of autologous cells and biomolecules such as platelet-rich plasma and their potential clinical applications.