Synthetic biology is an emerging field that strives to build increasingly complex biological networks through the integration of molecular biology and engineering. The growth of the field has been supported by progress in the design and construction of synthetic genetic and protein networks. This has led to the possibility of assembling modular components to attain novel biological functions and tools. In addition, these synthetic networks give rise to insights that facilitate the investigation of interactions and phenomena in naturally-occurring networks. Integration of well-characterized biological components into higher order networks requires computational modeling approaches to rationally construct systems that are directed towards a desired outcome. A computational approach would improve the predictability of the underlying mechanisms that would otherwise be difficult to deduce through experimentation alone. The analysis and interpretation of both qualitative and quantitative models also becomes increasingly important towards taking a systems-level perspective on synthetic genetic and protein networks. This review will first discuss the analogy of synthetic networks to circuit engineering. It will then look at computational modeling approaches that can be applied to biological systems and how synthetic biology will help to develop more accurate in silico representations of these systems.