Neurofeedback training using real-time functional magnetic resonance imaging (rtfMRI-NF) allows subjects voluntary control of localized and distributed brain activity. It has sparked increased interest as a promising non-invasive treatment option in neuropsychiatric and neurocognitive disorders, although its efficacy and clinical significance are yet to be determined. Maximization of neurofeedback learning effects in accordance with operant conditioning requires the feedback signal to be closely contingent on real brain activity, which necessitates the use of effective real-time fMRI denoising methods to prevent sham feedback. In this work we investigated the state of denoising and data quality control practices in rtfMRI-NF, focusing on a set of 99 recent studies as well as published real-time fMRI algorithms and toolboxes. We found that less than a third of the studies implemented a set of standard real-time fMRI denoising steps; poor adherence to best practices regarding methods reporting; and an absence of methodological studies quantifying and comparing the contribution of denoising steps to the quality of the neurofeedback signal. Additionally, only 6 out of 99 studies reported the use of advanced real-time physiological noise correction methods. Recognising an absence of curated information regarding denoising and quality in rtfMRI-NF, we reviewed a list of acquisition and data processing steps as well as data quality metrics available to researchers. Advances in the field of rtfMRI-NF research depend on reproducibility of methods and results. To this end, we recommend that future rtfMRI-NF studies report implementation, and motivate exclusion, of a set of standard real-time fMRI denoising steps; ensure the quality of the neurofeedback signal by calculating and reporting community-informed quality metrics and applying offline control checks; and adhere to open science principles of methods and data sharing and the use and development of open-source rtfMRI-NF software.