<p>Magnetic resonance imaging (MRI) plays a central role in diagnosing neurological diseases, offering non-invasive, high-resolution views of brain anatomy. However, manual interpretation remains labor-intensive and subject to variability, particularly when detecting subtle or diffuse abnormalities. The growing volume of imaging data and limited availability of expert annotations have driven interest in artificial intelligence (AI)-based automation. Traditional supervised learning in neuroimaging demand large, annotated datasets and often struggle to generalize due to disease heterogeneity. Anomaly detection has gained attention as a scalable alternative: it models normal brain anatomy and flags deviations as potential abnormalities—without relying on labor-intensive, expert-labeled data. Because brain neuroscience is inherently complex, anomaly detection offers distinct promise in neuroimaging. In this review, we map the field of brain MRI anomaly detection across traditional statistics, classical machine learning (ML), and contemporary deep learning. We organize deep-learning work into three paradigms—reconstruction, generative, and self-supervised—highlighting their core assumptions, advantages, and caveats. Even with recent advances, critical challenges persist—including high false positive rates, unclear definitions of abnormality, limited interpretability, and vulnerability to domain shifts. To address these issues, emerging strategies such as hybrid learning, multimodal integration, and biologically grounded metrics (e.g., brain age gap) show promise in improving robustness and clinical relevance. We conclude with a research agenda for developing generalizable and interpretable AI systems that integrate into real-world neuroimaging workflows. We intend this review to serve as a practical and comprehensive guide for researchers and clinicians advancing reliable, scalable brain-MRI anomaly detection.</p>