In August 2022 the Department of Health and Human Services (HHS) issued a notice of proposed rulemaking prohibiting covered entities, which include health care providers and health plans, from discriminating against individuals when using clinical algorithms in decision making. However, HHS did not provide specific guidelines on how covered entities should prevent discrimination. We conducted a scoping review of literature published during the period 2011-22 to identify health care applications, frameworks, reviews and perspectives, and assessment tools that identify and mitigate bias in clinical algorithms, with a specific focus on racial and ethnic bias. Our scoping review encompassed 109 articles comprising 45 empirical health care applications that included tools tested in health care settings, 16 frameworks, and 48 reviews and perspectives. We identified a wide range of technical, operational, and systemwide bias mitigation strategies for clinical algorithms, but there was no consensus in the literature on a single best practice that covered entities could employ to meet the HHS requirements. Future research should identify optimal bias mitigation methods for various scenarios, depending on factors such as patient population, clinical setting, algorithm design, and types of bias to be addressed.