Radiological incidental findings (IFs) are previously undetected abnormalities which are unrelated to the original indication for imaging and are unexpectedly discovered. In brain magnetic resonance imaging (MRI), the prevalence of IFs is increasing. By reviewing the literature on IFs in brain MRI performed for research purposes and discussing ethical considerations of IFs, this paper provides an overview of brain IF research results and factors contributing to inconsistencies and considers how the consent process can be improved from an ethical perspective. We found that despite extensive literature regarding IFs in research MRI of the brain, there are major inconsistencies in the reported prevalence, ranging from 1.3% to 99%. Many factors appear to contribute to this broad range: lack of standardised definition, participant demographics variance, heterogenous MRI scanner strength and sequences, reporter variation and results classification. We also found significant discrepancies in the review, consent and clinical communication processes pertaining to the ethical nature of these studies. These findings have implications for future studies, particularly those involving artificial intelligence. Further research, particularly in relation to MRI brain IFs would be useful to explore the generalisability of study results.