In this review, concepts of algorithmic bias and fairness are defined qualitatively and mathematically. Illustrative examples are given of what can go wrong when unintended bias or unfairness in algorithmic development occurs. The importance of explainability, accountability, and transparency with respect to artificial intelligence algorithm development and clinical deployment is discussed. These are grounded in the concept of primum no nocere (first, do no harm). Steps to mitigate unfairness and bias in task definition, data collection, model definition, training, testing, deployment, and feedback are provided. Discussions on the implementation of fairness criteria that maximize benefit and minimize unfairness and harm to neuroradiology patients will be provided, including suggestions for neuroradiologists to consider as artificial intelligence algorithms gain acceptance into neuroradiology practice and become incorporated into routine clinical workflow.