A summary of clinical background of MDD and BD, Brain structure and EEG based brain activity,• EEG experimental protocols study for mental disorders diagnosis,• An extensive study of state-of-the-art shallow and deep neural networks models for EEG based clinical depression detection,• An extensive study of neural networks based approaches for Biploar Disorder diagnosis using EEG signals,• A discussion of state-of-the-art methods limitations and giving valuable recommendations for future research