In the last decade, the brain's oscillatory responses have invaded the literature. The studies on delta (0.5-3.5Hz) oscillatory responses in humans upon application of cognitive paradigms showed that delta oscillations are related to cognitive processes, mainly in decision making and attentional processes. The present manuscript comprehensively reviews the studies on delta oscillatory responses upon cognitive stimulation in healthy subjects and in different pathologies, namely Alzheimer's disease, Mild Cognitive Impairment (MCI), bipolar disorder, schizophrenia and alcoholism. Further delta oscillatory response upon presentation of faces, facial expressions, and affective pictures are reviewed. The relationship between pre-stimulus delta activity and post-stimulus evoked and event-related responses and/or oscillations is discussed. Cross-frequency couplings of delta oscillations with higher frequency windows are also included in the review. The conclusion of this review includes several important remarks, including that delta oscillatory responses are involved in cognitive and emotional processes. A decrease of delta oscillatory responses could be a general electrophysiological marker for cognitive dysfunction (Alzheimer's disease, MCI, bipolar disorder, schizophrenia and alcoholism). The pre-stimulus activity (phase or amplitude changes in delta activity) has an effect on post-stimulus EEG responses.