Graph neural networks (GNNs) are increasingly used for medical imaging analysis and biological data modeling, where the integration of radiomics, topology, geometry, and generative artificial intelligence (AI) may improve representation learning from medical images and related biomedical data. Across the reviewed literature, GNNs show particular value for modeling spatial relationships, multimodal interactions, graph-structured biological networks, and non-Euclidean imaging features that are difficult to capture using conventional convolutional architectures alone. Topology- and geometry-aware approaches further expand this capability by encoding multi-scale structure, higher-order relationships, curvature, geodesic organization, and equivariant spatial priors. Hybrid graph–transformer models and generative graph methods represent emerging directions for modeling long-range dependencies, augmenting scarce datasets, supporting synthetic pretraining, and improving representation learning in low-label or heterogeneous biomedical settings. However, clinical translation remains limited by variability in graph construction, limited external validation, computational cost, scalability constraints, interpretability challenges, and uncertainty regarding the biological realism of synthetic data. Overall, this review highlights that GNN-based medical imaging analysis is most likely to advance when graph construction is biologically justified, model performance is evaluated across diverse clinical cohorts, and technical gains are paired with transparent validation, interpretability, and implementation strategies.