Summary: Gaussian graphical models are widely popular for studying the conditional dependence among random variables. By encoding conditional dependence as an undirected graph, Gaussian graphical models provide interpretable representations and insightful visualizations of the relationships among variables. However, time series data present additional challenges: the graphs can evolve over time – with changes occurring at unknown time points – and the data often exhibit heavy-tailed characteristics. To address these challenges, we propose dynamic and robust Bayesian graphical models that employ state-of-the-art hidden Markov models (HMMs) to introduce dynamics in the graph and heavy-tailed multivariate \(t\)-distributions for model robustness. The HMM latent states are linked both temporally and hierarchically for greater information sharing across time and between states. The proposed methods are computationally efficient and demonstrate excellent graph estimation on simulated data with substantial improvements over non-robust graphical models. We demonstrate our proposed approach on human hand gesture tracking data, and discover edges and dynamics with well explained practical meanings.