A major goal in systems biology is a comprehensive description of the entirety of all complex interactions between different types of biomolecules-also referred to as the interactome-and how these interactions give rise to higher, cellular and organism level functions or diseases. Numerous efforts have been undertaken to define such interactomes experimentally, for example yeast-two-hybrid based protein-protein interaction networks or ChIP-seq based protein-DNA interactions for individual proteins. To complement these direct measurements, genome-scale quantitative multi-omics data (transcriptomics, proteomics, metabolomics, etc.) enable researchers to predict novel functional interactions between molecular species. Moreover, these data allow to distinguish relevant functional from non-functional interactions in specific biological contexts. However, integration of multi-omics data is not straight forward due to their heterogeneity. Numerous methods for the inference of interaction networks from homogeneous functional data exist, but with the advent of large-scale paired multi-omics data a new class of methods for inferring comprehensive networks across different molecular species began to emerge. Here we review state-of-the-art techniques for inferring the topology of interaction networks from functional multi-omics data, encompassing graphical models with multiple node types and quantitative-trait-loci (QTL) based approaches. In addition, we will discuss Bayesian aspects of network inference, which allow for leveraging already established biological information such as known protein-protein or protein-DNA interactions, to guide the inference process.