Complex patterns of behavior are common in many biological networks, where no single agent is in command and yet forms of decentralized intelligence are evident. Examples include fish joining together in schools, birds flying in formation, bees swarming towards a new hive, and bacteria diffusing towards a nutrient source. While each individual agent in these biological networks is not capable of complex behavior, it is the combined coordination among multiple agents that leads to the manifestation of sophisticated order at the network level. The study of these phenomena opens up opportunities for collaborative research across several domains including economics, life sciences, biology, and information processing, in order to address and clarify several relevant questions such as: (a) how and why organized behavior arises at the group level from interactions among agents without central control? (b) What communication topologies enable the emergence of order at the higher level from interactions at the lower level? (c) How is information quantized during the diffusion of knowledge through the network? And (d) how does mobility influence the learning abilities of the agents and the network. Several disciplines are concerned in elucidating different aspects of these questions including evolutionary biology, animal behavior studies, physical biology, and even computer graphics. In the realm of signal processing, these questions motivate the need to study and develop decentralized strategies for information processing that are able to endow networks with real-time adaptation and learning abilities. This presentation examines several patterns of decentralized intelligence in biological networks, and describes diffusion adaptation and learning strategies that our research group has developed in recent years to model and reproduce these kinds of behavior.