No matter how well we understand the behavior of a single water droplet in the laboratory, we cannot predict how myriads of them assemble into clouds and rain, with significant impact on our climate. And although one can precisely record the electric pulses of a neuron, no one understands today how billions of them together form a thought. This is the realm of self-organization, where plenty of interacting parts organize themselves into a complex whole, without external control. The Max Planck Institute for Dynamics and Self-Organization is investigating the fundamental mechanisms of these interactions in order to obtain a detailed understanding of complex systems in general.