Adaptive networks consist of a collection of agents with adaptation and learning abilities. The agents interact with each other on a local level and diffuse information across the network to solve estimation, inference, and optimization tasks in a fully distributed manner. Some surprising phenomena arise when information is processed over networks in a distributed manner. In this talk, we describe two such phenomena. In the first case, we consider two types of agents: informed agents and uninformed agents. The former receive data regularly and perform neighbor consultation and in-network processing, while the latter do not collect data and only participate in the consultation tasks. We examine the performance of networks as a function of the proportion of informed agents.The results reveal a surprising trade-off between convergence rate and mean-square performance. In particular, it will be seen that the performance of distributed networks does not necessarily improve with a larger proportion of informed agents. It will also be seen that it is preferable to maintain some of the highly connected agents in an uninformed state, and that even uninformed agents have a role to play. The second phenomenon that we consider reveals that the order by which information is processed at the nodes is critical; minor variations can lead to catastrophic failure even when all nodes are stable. To illustrate this effect, we compare the behavior of two strategies for distributed estimation: consensus strategies and diffusion strategies. It will be seen that diffusion strategies allow information to diffuse more thoroughly through the network and attain lower mean-square error. Moreover, the stability of diffusion networks is insensitive to the topology and to the choice of the combination weights. In contrast, and surprisingly, consensus networks can become unstable even if all the individual nodes are stable. When this occurs, cooperation over the network fails to solve the inference task. This phenomenon does not occur for diffusion networks: stability of the individual nodes always ensures stability of the diffusion network irrespective of the topology. In addition, diffusion strategies do not require the network to be strongly connected; diffusion implementations continue to deliver performance even if the network becomes disconnected into disjoint subgroups. These results indicate that information flow over networks is influenced by several factors in some revealing ways: the proportion of informed agents, the location of these agents, and how they process and disseminate information through the network.