A growing body of research addressed fundamental ethical concerns for AI-driven recruitment. They Highlight specifically transparency, and accountability concerns. These issues impact highly the fairness and performance of recruitment and consequently the acceptability of AI among end-users particularly candidates as a pivotal stakeholder in the recruitment process. In the absence of appropriate ethical oversight, AI-driven recruitment tools risk delivering discriminatory results, leading to reduce trust and inhibit consequently adoption. The aim of this review is to analyze the impact of bias on the performance and acceptance of the technology to provide a structured approach based on Fair Machine Learning (FairML) principles, which enable a control over ethical challenges. It further explores how FairML principles theoretically frame the key components of responsible AI-based recruitment.