Virtual brain modeling is a data-driven approach that combines personalized anatomical information with mathematical models of brain activity to generate spatiotemporal patterns as observed in brain imaging signals. In this study our aim is to conduct inference and prediction on the local and global dynamics using virtual brain models, affected by disorders. Inference algorithms are necessary to efficiently estimate the unknown parameters (such as regional excitability parameters and global scaling factor on connectome), ideally incorporating measures of uncertainty. In this work, we provide flexible and efficient Bayesian inference on virtual brain models using state-of-the-art algorithms (Monte Carlo sampling and deep neural density estimators). We show the benefits of incorporating prior information and inference diagnostics, using self-tuning Monte Carlo strategies for exact statistical inference, as well as deep learning algorithms for fast and efficient model inversion. The performance of these methods is then demonstrated on causal inference and prediction in various brain disorders, such as epilepsy, alcohol use disorder, multiple sclerosis, and Alzheimer's disease.