Neurological/neurovascular disorders constitute the leading cause of disability and the second leading cause of death globally. Major neurological/neurovascular disorders or diseases include cerebral stroke, Alzheimer’s disease, spinal cord injury, neonatal hypoxic-ischemic encephalopathy, and others. Their pathophysiology is considered highly complex and is the main obstacle in developing any drugs for these diseases. In this review, we have described the endothelin system, its involvement in neurovascular disorders, the importance of endothelin B receptors (ETBRs) as a novel potential drug target, and its agonism by IRL-1620 (INN—sovateltide), which we are developing as a drug candidate for treating the above-mentioned neurological disorders/diseases. In addition, we have highlighted the results of our preclinical and clinical studies related to these diseases. The phase I safety and tolerability study of sovateltide has shown it as a safe and tolerable compound at therapeutic dosages. Furthermore, preclinical and clinical phase II studies have demonstrated the efficacy of sovateltide in treating acute ischemic stroke. It is under development as a first-in-class drug. In addition, efficacy studies in Alzheimer’s disease (AD), acute spinal cord injury, and neonatal hypoxic-ischemic encephalopathy (HIE) are ongoing. Successful completion of these studies will validate that ETBRs signaling can be an important target in developing drugs to treat neurological/neurovascular diseases.