Ensuring that machine learning (ML) models are safe, effective, and equitable across all patients is critical for clinical decision-making and for preventing the amplification of existing health disparities. In this work, we examine how fairness is conceptualized in ML for health, including why ML models may lead to unfair decisions and how fairness has been measured in diverse real-world applications. We review commonly used fairness notions within group, individual, and causal-based frameworks. We also discuss the outlook for future research and highlight opportunities and challenges in operationalizing fairness in health-focused applications.