Improved treatment options are urgently needed for neurological injuries resulting from trauma or iatrogenic events causing long-term disabilities that severely impact patients’ quality of life. In vitro and animal studies have provided promising proof-of-concept examples of regenerative therapies using mesenchymal stromal cells (MSC) for a wide range of pathological conditions. Over the previous decade, various MSC-based therapies have been investigated in clinical trials to treat traumatic neurological injuries. However, while the safety and feasibility of MSC treatments has been established, the patient outcomes in these studies have not demonstrated significant success in the translation of MSC regenerative therapy for the treatment of human brain and spinal cord injuries. Herein, we have reviewed the literature and ongoing registered trials on the application of MSC for the treatment of traumatic brain injury, traumatic spinal cord injury, and peripheral nerve injury. We have focused on the shortcomings and technological hurdles that must be overcome to further advance clinical research to phase 3 trials, and we discuss recent advancements that represent potential solutions to these obstacles to progress.