The crises of the last years have underlined how much the modern financial systems are today more exposed and vulnerable to systemic risk, defined as the risk of uncontrolled propagation of a crisis of a single player or area of an economic system to a wider system through contagion mechanisms. Systemic risk is more relevant today than in the past due to the increasing interconnection between the players in the economic system and the increasing speed of flows of goods, money and people. All this prompts us to reflect on the need to analyse, predict and manage systemic risk holistically and through the logical-conceptual schemes that can be borrowed from network science.