BrainWave Diagnostics, an emerging field, leverages electroencephalography (EEG) data for cost-effective and resource-efficient neurological disorder detection. Although EEGs are commonly used for neurological disease detection, their low signal intensity and nonlinear features pose analytical challenges. This review explores the use of high-performance computational tools, machine learning, and deep learning methods in diagnosing a range of neurological disorders, including epilepsy, Parkinson's disease, autism, ADHD, stroke, tumors, schizophrenia, Alzheimer's, depression, and alcohol use disorder. The increasing prevalence of neurological disorders and their resource burden underscores the urgency of these diagnostic advancements. Future research can consider multi-modal approaches, providing practical solutions for neurological disorder detection beyond EEGs, with potential applications in diverse signal analysis domains.