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Degenerative nerve diseases such as Alzheimer's and Parkinson's diseases have always been a global issue of concern. Approximately 1/6th of the world's population suffers from these disorders, yet there are no definitive solutions to cure these diseases after the symptoms set in. The best way to treat these disorders is to detect them at an earlier stage. Many of these diseases are genetic; this enables machine learning algorithms to give inferences based on the patient's medical records and history. Machine learning algorithms such as deep neural networks are also critical for the early identification of degenerative nerve diseases. The significant applications of machine learning and deep learning in early diagnosis and establishing potential therapies for degenerative nerve diseases have motivated us to work on this review paper. Through this review, we covered various machine learning and deep learning algorithms and their application in the diagnosis of degenerative nerve diseases, such as Alzheimer's disease and Parkinson's disease. Furthermore, we also included the recent advancements in each of these models, which improved their capabilities for classifying degenerative nerve diseases. The limitations of each of these methods are also discussed. In the conclusion, we mention open research challenges and various alternative technologies, such as virtual reality and Big data analytics, which can be useful for the diagnosis of degenerative nerve diseases. [ABSTRACT FROM AUTHOR]