The increasing application of network models to interpret biological systems raises a number of important methodological and epistemological questions. What novel insights can network analysis provide in biology? Are network approaches an extension of or in conflict with mechanistic research strategies? When and how can network and mechanistic approaches interact in productive ways? In this paper we address these questions by focusing on how biological networks are represented and analyzed in a diverse class of case studies. Our examples span from the investigation of organizational properties of biological networks using tools from graph theory to the application of dynamical systems theory to understand the behavior of complex biological systems. We show how network approaches support and extend traditional mechanistic strategies but also offer novel strategies for dealing with biological complexity.