The living world is made up of complex biological systems. At the level of the individual, the most complex of these systems is the human brain. But the process of evolution has produced even more complex systems, such as tropical reefs and rainforests, that are made up of millions of interacting species. How has this complexity evolved? Recent advances in our understanding of evolution have revealed important genetic and ecological processes that all these complex systems have in common. The evolution of the human brain has been driven by a feedback loop between our brains, our genes and our highly challenging environment. We will look at some of the genes that are involved in this process to see how they have changed during our recent evolutionary history. We will also see how a process called frequency-dependent selection has made all of our brains slightly different from each other, so that collectively as a species we can accomplish far more than a single individual ever could. Our research group has recently shown that this same process of frequency-dependent selection has driven the evolution of tropical rainforests. We will see how this evolutionary process has built up the diversity of these fragile ecosystems, so that, just as with our brains, these vast collections of species can do far more than a less species-rich ecosystem possibly could. Finally we will look at the fragility of these complex ecosystems. In collaboration with tropical ecologists worldwide, we have now demonstrated that a small reduction in the complexity of tropical rainforests will have a substantial negative impact on the growth and survival of the remaining species. The value of complexity and diversity in the natural world is high, and we put ourselves at risk if we do not maintain it.