Simultaneous electroencephalography-functional MRI (EEG-fMRI) is a technique that combines temporal (largely from EEG) and spatial (largely from fMRI) indicators of brain dynamics. It is useful for understanding neuronal activity during many different event types, including spontaneous epileptic discharges, the activity of sleep stages, and activity evoked by external stimuli and decision-making tasks. However, EEG recorded during fMRI is subject to imaging, pulse, environment and motion artifact, causing noise many times greater than the neuronal signals of interest. Therefore, artifact removal methods are essential to ensure that artifacts are accurately removed, and EEG of interest is retained. This paper presents a systematic review of methods for artifact reduction in simultaneous EEG-fMRI from literature published since 1998, and an additional systematic review of EEG-fMRI studies published since 2016. The aim of the first review is to distill the literature into clear guidelines for use of simultaneous EEG-fMRI artifact reduction methods, and the aim of the second review is to determine the prevalence of artifact reduction method use in contemporary studies. We find that there are many published artifact reduction techniques available, including hardware, model based, and data-driven methods, but there are few studies published that adequately compare these methods. In contrast, recent EEG-fMRI studies show overwhelming use of just one or two artifact reduction methods based on literature published 15–20 years ago, with newer methods rarely gaining use outside the group that developed them. Surprisingly, almost 15% of EEG-fMRI studies published since 2016 fail to adequately describe the methods of artifact reduction utilized. We recommend minimum standards for reporting artifact reduction techniques in simultaneous EEG-fMRI studies and suggest that more needs to be done to make new artifact reduction techniques more accessible for the researchers and clinicians using simultaneous EEG-fMRI.