How should we understand the new digital media and the effect of digital networks on global communication? Medium theory would be an obvious candidate, suggesting that we are in the middle of a transition from a society based on analogue media (print and electronic) to a society based on digital media. However, the present article suggests we examine another candidate: complexity theory. According to writers such as John Urry, we are in the middle of a paradigm turn, the so-called complexity turn. The aim of this article is to discuss whether complexity theory can be applied to media studies. What are the gains, and what would we lose? The author takes as his point of departure two case examples. The first is the case of the Mohammed cartoons in the Danish newspaper Jyllands- Posten. The second is the case of the Internet. How are we to understand the Internet as a qualitatively new medium? The author goes on to present two fundamental concepts of complexity theory. The first is the concept of complexity. The second is the concept of mediated communication, which appears to change significance in the context of complexity theory.