Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the variousbiological processes for intuitive and rigorous understanding and interpretations. In the context of largenetworks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. Thesefeatures are particularly important in applications with limited sample size, including genomics andimaging studies. In this paper, we review several recently developed techniques for the analysis of largenetworks under non-standard settings, including but not limited to, multiple graphs for data observedfrom multiple related subgroups, graphical regression approaches used for the analysis of networks thatchange with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.