A Comprehensive Review of Functional Graphical Models

Functional graphical models (FGMs) extend classical graphical models from multivariate vectors to multivariate random functions, enabling inference on conditional dependence and, in directed settings, directional or causal relationships across functional domains. This review provides a unified overview of recent developments in both undirected and directed FGMs. We summarize key theoretical foundations, estimation methods, and computational challenges arising from infinite dimensionality, operator non‐invertibility, dimension reduction, and non‐Gaussian behavior. Applications in brain connectivity, protein signaling, transportation systems, and longitudinal microbiome studies illustrate the broad potential of FGMs. We also highlight open research directions, including dynamic networks, adaptive truncation, and methodological extensions beyond Gaussian assumptions.