Graph generative models are gaining significant interest in different application domains. They are commonly used to model social networks, knowledge graphs, medical data and bio/chemical networks. In this talk we will present the main methods for graph generative models and our recent relevant efforts in the biomedical domain. More specifically we present a novel architecture that generates medical records as graphs with privacy guarantees. We capitalize and modify the Graph Variational autoencoders (GVAEs) architecture. We train the generative model with the well known MIMIC medical database and achieve credible generated data. We also develop new GNNs for predicting antibiotic resistance and other protein related downstream tasks such as enzymes classifications and Gene Ontology classification. We achieve there as well promising results with potential for future application in broader biomedical related tasks. Finally we present interesting research directions for multi modal generative models involving graphs with applications in diverse domains.