The rapid migration of organizational workloads to cloud environments has introduced unprecedented scalability but also significant financial complexity. Cloud billing is often characterized by high-volume, granular data where \\\"anomalies\\\"—unexpected spikes or shifts in spending—can remain undetected for weeks, leading to \\\"cloud sprawl\\\" and budget overruns. Traditional threshold-based monitoring systems often fail in these dynamic environments due to their inability to distinguish between legitimate scaling and genuine waste. This article reviews the shift toward Machine Learning (ML)-centric approaches for cloud cost anomaly detection. By leveraging time-series forecasting, clustering, and deep learning, ML models can learn the \\\"seasonal\\\" rhythms of business operations and flag deviations with high precision. This review explores the architectural foundations of these systems, evaluates supervised versus unsupervised learning paradigms, and discusses the operational challenges of implementing AI-driven FinOps. Ultimately, the integration of ML transforms cost management from a reactive reporting task into a proactive, automated defense mechanism, ensuring operational stability and financial efficiency in modern cloud-native architectures.