Functional genomics has enormous potential to facilitate our understanding of normal and disease-specific physiology. In the past decade, intensive research efforts have been focused on modeling functional relationship networks, which summarize the probability of gene co-functionality relationships. Such modeling can be based on either expression data only or heterogeneous data integration. Numerous methods have been deployed to infer the functional relationship networks, while most of them target the global (non-context-specific) functional relationship networks. However, it is expected that functional relationships consistently reprogram under different tissues or biological processes. Thus, advanced methods have been developed targeting tissue-specific or developmental stage-specific networks. This article brings together the state-of-the-art functional relationship network modeling methods, emphasizes the need for heterogeneous genomic data integration and context-specific network modeling and outlines future directions for functional relationship networks.