The electroencephalogram (EEG) is a fundamental tool in the diagnosis and classification of epilepsy. In particular, Interictal Epileptiform Discharges (IEDs) reflect an increased likelihood of seizures and are routinely assessed by visual analysis of the EEG. Visual assessment is, however, time consuming and prone to subjectivity, leading to a high misdiagnosis rate and motivating the development of automated approaches. Research towards automating IED detection started 45 years ago. Approaches range from mimetic methods to deep learning techniques. We review different approaches to IED detection, discussing their performance and limitations. Traditional machine learning and deep learning methods have yielded the best results so far and their application in the field is still growing. Standardization of datasets and outcome measures is necessary to compare models more objectively and decide which should be implemented in a clinical setting.