Chronic low back pain (LBP) remains a challenging condition to treat, and especially to cure. If conservative treatment approaches fail, the current “gold standard” for intervertebral disc degeneration (IDD)-provoked back pain is spinal fusion. However, due to its invasive and destructive nature, the focus of orthopedic research related to the intervertebral disc (IVD) has shifted more towards cell-based therapeutic approaches. They aim to reduce or even reverse the degenerative cascade by mimicking the human body’s physiological healing system. The implementation of progenitor and/or stem cells and, in particular, the delivery of mesenchymal stromal cells (MSCs) has revealed significant potential to cure the degenerated/injured IVD. Over the past decade, many research groups have invested efforts to find ways to utilize these cells as efficiently and sustainably as possible. This narrative literature review presents a summary of achievements made with the application of MSCs for the regeneration of the IVD in recent years, including their preclinical and clinical applications. Moreover, this review presents state-of-the-art strategies on how the homing capabilities of MSCs can be utilized to repair damaged or degenerated IVDs, as well as their current limitations and future perspectives.