The benefits of early detection and classification of epileptic seizures in analysis, monitoring and diagnosis for the realization and actualization of computer-aided devices and recent internet of medical things (IoMT) devices can never be overemphasized. The success of these applications largely depends on the accuracy of the detection and classification techniques employed. Several methods have been investigated, proposed and developed over the years. This paper investigates various seizure detection algorithms and classifications in the last decade, including conventional techniques and recent deep learning algorithms. It also discusses epileptiform detection as one of the steps towards advanced diagnoses of disorders of consciousness (DOCs) and their understanding. A performance comparison was carried out on the different algorithms investigated, and their advantages and disadvantages were explored. From our survey, much attention has recently been paid to exploring the efficacy of deep learning algorithms in seizure detection and classification, which are employed in other areas such as image processing and classification. Hybrid deep learning has also been explored, with CNN-RNN being the most popular.