EEG recorded during fMRI is subject to artefact many times greater than neuronal events of interest, therefore, artefact removal methods are crucial for accurate EEG-fMRI studies. This work systematically reviews all novel artefact reduction methods (1998-2018), as well as the use of artefact reduction methods (2016-2018). Results show that whilst there are many published artefact reduction methods, contemporary studies overwhelmingly use only a few established methods. It is recommended that: 1. Artefact reduction techniques are adequately reported, 2. Novel software is robust to help adoption by others, and 3. Commercial EEG-fMRI vendors consider including additional hardware for recording artefact.