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 and learning abilities at the network level. The study of these phenomena opens up opportunities for collaborative research across several domains including economics, life sciences, biology, machine learning, and information processing, in order to address and clarify several relevant questions such as: (a) how and why organized and complex 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 and tracking abilities of the agents and the network. Several disciplines are concerned in elucidating different aspects of these questions including evolutionary biology, animal behavior programs, physical biology, and also computer graphics. In the realm of machine learning and signal processing, these questions motivate the need to study and develop decentralized strategies for information processing that are able to endow cognitive networks with real-time adaptation and learning abilities. Cognitive networks consist of spatially distributed agents that are linked together through a connection topology. The topology may vary with time and the agents may also move. The agents cooperate with each other through local interactions and by means of in-network processing. Such networks are well-suited to perform decentralized information processing, decentralized optimization, and decentralized learning and inference tasks. They are also well-suited to model and understand self-organized and complex behavior encountered in nature and in social and economic networks. This presentation examines several patterns of decentralized intelligence in biological networks, and describes powerful diffusion adaptation and online learning strategies that our research group has been developing in recent years to model and reproduce these kinds of learning behavior over cognitive networks.