Biological systems, from embryos to social insects, get tremendous mileage by having vast numbers of cheap and unreliable individuals cooperate to achieve complex goals. We are also rapidly building new kinds of distributed systems with similar characteristics, from multi-modular robots and robot swarms, to vast sensor networks. Can we engineer collective systems to achieve the kind of complexity and self-repair that nature seems to achieve? In this talk, I will describe several projects from my group where we have used inspiration from nature -- termites, fireflies, and cells -- to design new kinds of robots and networks. For example, simple robots that collectively build structures without explicit communication, self-adaptive modular robots that respond to the environment, and wireless sensor networks that use firefly-inspired algorithms to achieve high throughput. In each case, we use inspiration from biology to design simple decentralized cooperation, and techniques from computer science to analyze and generalize these algorithms to new tasks. A common theme in all of our work is understanding self-organizing multi-agent systems: how does robust collective behavior arise from many locally interacting agents, and how can we systematically program simple agents to achieve the global behaviors we want.