Recent development of bio-technologies such as microarrays and high-throughput sequencing has greatly accelerated the pace of genetics experimentation and discoveries. As a result, large amounts of high-dimensional genomic data are available in population genetics and medical genetics. With millions of biomarkers, it is a very challenging problem to search for the disease-associated or treatment-associated markers, and infer the complicated interaction (correlation) patterns among these markers. In this talk, we present Bayesian inference of interactions in two biological research areas: HIV drug resistance studies, and whole-genome association studies of common diseases, and we will also present a new recursive Bayesian algorithm for BN structure. We have investigated the HIV drug resistance problem from a new perspective. By probabilistically modeling mutations in the HIV-1 proteases isolated from drug-treated patients, we have derived a statistical procedure that first detects potentially complicated mutation combinations and then infers detailed interacting structures of these mutations. We have developed a Bayesian model for simultaneously inferring haplotypeblocks and selecting SNPs within blocks that are associated with the disease, either individually, or through epistatic interactions with others. Simulation results show that this approach is uniformly more powerful than other epistasis mapping methods. Applying this method to Type 1 Diabetes data, we landscape the interaction patterns in MHC region for this disease. Finally, the idea of recursively exploring the dependence structure of interactions in the above two research studies can be generalized to infer the structure of graph models.