The expanding adoption of artificial intelligence systems across high-impact sectors has catalyzed concerns regarding inherent biases and discrimination, leading to calls for greater transparency and accountability. Algorithm auditing has emerged as a pivotal method to assess fairness and mitigate risks in applied machine learning models. This systematic literature review comprehensively analyzes contemporary techniques for auditing the biases of black-box AI systems beyond traditional software testing approaches. An extensive search across technology, law, and social sciences publications identified 22 recent studies exemplifying innovations in quantitative benchmarking, model inspections, adversarial evaluations, and participatory engagements situated in applied contexts like clinical predictions, lending decisions, and employment screenings. A rigorous analytical lens spotlighted considerable limitations in current approaches, including predominant technical orientations divorced from lived realities, lack of transparent value deliberations, overwhelming reliance on one-shot assessments, scarce participation of affected communities, and limited corrective actions instituted in response to audits. At the same time, directions like subsidiarity analyses, human-cent