Systems incorporating biometric technologies have become ubiquitous in personal, commercial, and governmental identity management applications. Both cooperative (e.g., access control) and noncooperative (e.g., surveillance and forensics) systems have benefited from biometrics. Such systems rely on the uniqueness of certain biological or behavioral characteristics of human beings, which enable for individuals to be reliably recognized using automated algorithms. Recently, however, there has been a wave of public and academic concerns regarding the existence of systemic bias in automated decision systems (including biometrics). Most prominently, face recognition algorithms have often been labeled as "racist" or "biased" by the media, nongovernmental organizations, and researchers alike. The main contributions of this article are: 1) an overview of the topic of algorithmic bias in the context of biometrics; 2) a comprehensive survey of the existing literature on biometric bias estimation and mitigation; 3) a discussion of the pertinent technical and social matters; and 4) an outline of the remaining challenges and future work items, both from technological and social points of view.