Neurological disorders represent significant global health challenges, driving the advancement of brain signal analysis methods. Scalp electroencephalography (EEG) and intracranial electroencephalography (iEEG) are widely used to diagnose and monitor neurological conditions. However, dataset heterogeneity and task variations pose challenges in developing robust deep learning solutions. This review systematically examines recent advances in deep learning approaches for EEG/iEEG-based neurological diagnostics, focusing on applications across 7 neurological conditions using 46 datasets. We explore trends in data utilization, model design, and task-specific adaptations, highlighting the importance of pre-trained multi-task models for scalable, generalizable solutions. To advance research, we propose a standardized benchmark for evaluating models across diverse datasets to enhance reproducibility. This survey emphasizes how recent innovations can transform neurological diagnostics and enable the development of intelligent, adaptable healthcare solutions.