Epilepsy is a neurological disorder of the brain that causes frequent occurrence of seizures. Electroencephalography (EEG) is a tool that assists neurologists in detecting epileptic seizures caused by an unexpected flow of electrical activities in the brain. Automated detection of an epileptic seizure is a crucial task in diagnosing epilepsy which overcomes the drawback of a visual diagnosis. The dataset analyzed in this article, collected from Children’s Hospital Boston (CHB) and the Massachusetts Institute of Technology (MIT), contains long-term EEG records from 24 pediatric patients. This review paper focuses on various patient-dependent and patient-independent personalized medicine approaches involved in the computer-aided diagnosis of epileptic seizures in pediatric subjects by analyzing EEG signals, thus summarizing the existing body of knowledge and opening up an enormous research area for biomedical engineers. This review paper focuses on the features of four domains, such as time, frequency, time-frequency, and nonlinear features, extracted from the EEG records, which were fed into several classifiers to classify between seizure and non-seizure EEG signals. Performance metrics such as classification accuracy, sensitivity, and specificity were examined, and challenges in automatic seizure detection using the CHB-MIT database were addressed.