Existing facial analysis systems have been shown to yield biased results against certain demographic subgroups. Due to its impact on society, it has become imperative to ensure that these systems do not discriminate based on gender, identity, or skin tone of individuals. This has led to research in the identification and mitigation of bias in AI systems. In this paper, we encapsulate bias detection/estimation and mitigation algorithms for facial analysis. Our main contributions include a systematic review of algorithms proposed for understanding bias, along with a taxonomy and extensive overview of existing bias mitigation algorithms. We also discuss open challenges in the field of biased facial analysis.