Affective computing, a subcategory of artificial intelligence, detects, processes, interprets, and mimics human emotions. Thanks to the continued advancement of portable non-invasive human sensor technologies, like brain–computer interfaces (BCI), emotion recognition has piqued the interest of academics from a variety of domains. Facial expressions, speech, behavior (gesture/posture), and physiological signals can all be used to identify human emotions. However, the first three may be ineffectual because people may hide their true emotions consciously or unconsciously (so-called social masking). Physiological signals can provide more accurate and objective emotion recognition. Electroencephalogram (EEG) signals respond in real time and are more sensitive to changes in affective states than peripheral neurophysiological signals. Thus, EEG signals can reveal important features of emotional states. Recently, several EEG-based BCI emotion recognition techniques have been developed. In addition, rapid advances in machine and deep learning have enabled machines or computers to understand, recognize, and analyze emotions. This study reviews emotion recognition methods that rely on multi-channel EEG signal-based BCIs and provides an overview of what has been accomplished in this area. It also provides an overview of the datasets and methods used to elicit emotional states. According to the usual emotional recognition pathway, we review various EEG feature extraction, feature selection/reduction, machine learning methods (e.g., k-nearest neighbor), support vector machine, decision tree, artificial neural network, random forest, and naive Bayes) and deep learning methods (e.g., convolutional and recurrent neural networks with long short term memory). In addition, EEG rhythms that are strongly linked to emotions as well as the relationship between distinct brain areas and emotions are discussed. We also discuss several human emotion recognition studies, published between 2015 and 2021, that use EEG data and compare different machine and deep learning algorithms. Finally, this review suggests several challenges and future research directions in the recognition and classification of human emotional states using EEG.