<p>Unintended biases introduced by optimization and machine learning models (a core area of artificial intelligence) are of great interest to medical researchers and professionals. Bias in healthcare decisions can cause patients from vulnerable populations (e.g., racially minoritized, low-income, or living in rural areas) to have lower access to resources and inferior outcomes, exacerbating societal unfairness. In this paper, we present a systematic review of the literature regarding fair decision making in healthcare until April 2024. We screened 801 unique references, identifying 114 articles within the scope. In our review, we examine fair decision-making methodologies in healthcare by systematically identifying and categorizing biases within both data and models. Additionally, we present a range of fairness metrics drawn from different use cases and classify bias mitigation strategies into pre-processing, in-processing, and post-processing techniques. We provide a broad conceptual overview and practical illustrations of each approach. Moreover, we examine emerging bias mitigation technologies that, though not yet applied in healthcare, show substantial promise for future integration. Our review aims to increase awareness of fairness in healthcare decision making and facilitate the selection of appropriate approaches under varying scenarios.</p>