Brain interictal epileptiform discharges (IEDs), as one of the hallmarks of epileptic brain, are transient events captured by electroencephalogram (EEG). IEDs are generated by seizure networks, and they occur between seizures (interictal periods). The development of a robust method for IED detection could be highly informative for clinical treatment procedures and epileptic patient management. Since 1972, different machine learning techniques, from template matching to deep learning, have been developed to automatically detect IEDs from scalp EEG (scEEG) and intracranial EEG (iEEG). While the scEEG signals suffer from low information details and high attenuation of IEDs due to the high skull electrical impedance, the iEEG signals recorded using implanted electrodes enjoy higher details and are more suitable for identifying the IEDs. In this review paper, we group IED detection techniques into six categories: (1) template matching, (2) feature representation (mimetic, time-frequency, and nonlinear features), (3) matrix decomposition, (4) tensor factorization, (5) neural networks, and (6) estimation of the iEEG from the concurrent scEEG followed by detection and classification. The methods are compared quantitatively (e.g., in terms of accuracy, sensitivity, and specificity), and their general advantages and limitations are described. Finally, current limitations and possible future research paths related to this field are mentioned.