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Electroencephalography (EEG) has countless applications across many of fields. However, EEG applications are limited by low signal-to-noise ratios. Multiple types of artifacts contribute to the noisiness of EEG, and many techniques have been proposed to detect and correct these artifacts. These techniques range from simply detecting and rejecting artifact ridden segments, to extracting the noise component from the EEG signal. In this paper we review a variety of recent and classical techniques for EEG data artifact detection and correction with a focus on the last half-decade. We compare the strengths and weaknesses of the approaches and conclude with proposed future directions for the field.