Epilepsy is a serious chronic neurological disorder, can be detected by analyzing the brain signals produced by brain neurons. Neurons are connected to each other in a complex way to communicate with human organs and generate signals. The monitoring of these brain signals is commonly done using Electroencephalogram (EEG) and Electrocorticography (ECoG) media. These signals are complex, noisy, non-linear, non-stationary and produce a high volume of data. Hence, the detection of seizures and discovery of the brain-related knowledge is a challenging task. Machine learning classifiers are able to classify EEG data and detect seizures along with revealing relevant sensible patterns without compromising performance. As such, various researchers have developed number of approaches to seizure detection using machine learning classifiers and statistical features. The main challenges are selecting appropriate classifiers and features. The aim of this paper is to present an overview of the wide varieties of these techniques over the last few years based on the taxonomy of statistical features and machine learning classifiers-'black-box' and 'non-black-box'. The presented state-of-the-art methods and ideas will give a detailed understanding about seizure detection and classification, and research directions in the future.