Network architecture plays a crucial role in governing the dynamics of any biological network. Further, network structures have been shown to remain conserved across organisms for a given phenotype. Therefore, the mapping between network structures and the output functionality not only aids in understanding of biological systems but also finds application in synthetic biology and therapeutics. Based on the approaches involved, most of the efforts hitherto invested in this field can be classified into three broad categories, namely, computational efforts, rule-based methods and systems-theoretic approaches. The present review provides a qualitative and quantitative study of all three approaches in the light of three well-researched biological phenotypes, namely, oscillation, toggle switching, and adaptation. We also discuss the advantages, limitations, and future research scope for all three approaches along with their possible applications to other emergent properties of biological relevance.