For decades, molecular biologists have been uncovering the mechanics of biological systems. Efforts to bring their findings together have led to the development of multiple databases and information systems that capture and present pathway information in a computable network format. Concurrently, the advent of modern omics technologies has empowered researchers to systematically profile cellular processes across different modalities. Numerous algorithms, methodologies, and tools have been developed to use prior knowledge networks in the analysis of omics datasets. Interestingly, it has been repeatedly demonstrated that the source of prior knowledge can greatly impact the results of a given analysis. For these methods to be successful it is paramount that their selection of prior knowledge networks is amenable to the data type and the computational task they aim to accomplish. Here we present a five-level framework that broadly describes network models in terms of their scope, level of detail, and ability to inform causal predictions. To contextualize this framework, we review a handful of network-based omics analysis methods at each level, while also describing the computational tasks they aim to accomplish.