Availability of large-scale experimental data for cell biology is enabling computational methods to systematically model the behaviour of cellular networks. This review surveys the recent advances in the field of graph-driven methods for analysing complex cellular networks. The methods are outlined on three levels of increasing complexity, ranging from methods that can characterize global or local structural properties of networks to methods that can detect groups of interconnected nodes, called motifs or clusters, potentially involved in common elementary biological functions. We also briefly summarize recent approaches to data integration and network inference through graph-based formalisms. Finally, we highlight some challenges in the field and offer our personal view of the key future trends and developments in graph-based analysis of large-scale datasets.