Adaptive networks consist of a collection of agents with local adaptation and learning abilities. The agents interact with each other on a local level and diffuse information across the network to solve inference or optimization tasks in a decentralized manner. Such networks are robust to node and link failures, and are particularly suitable for learning from large data sets by tapping into the power of cooperation among spatially-distributed agents. Nevertheless, some surprising phenomena arise when information is processed in a decentralized fashion over networked systems. For example, the addition of more informed agents does not necessarily lead to enhanced performance, and even minor variations in how information is processed by the agents can lead to failure. In this talk, we elaborate on such phenomena in the context of distributed stochastic-gradient learners. We consider two classes of distributed schemes for learning and adaptation involving consensus strategies and diffusion strategies. We quantify how the performance and the convergence rate of the network vary with the combination policy and with the proportion of informed agents, and explain how the performance of any arbitrary connected topology can be made to match the performance of centralized stochastic learners. Among other results, it will be seen that the performance of a network of learners does not always improve with a larger proportion of informed agents. A strategy to counter the degradation in performance is presented. It will also be seen how the order by which information is processed by the agents is critical: minor variations can lead to failure even in situations when the agents are able to solve the inference task individually on their own. To illustrate these effects, we will establish that diffusion protocols are mean-square stable regardless of the network topology. In contrast, consensus protocols can become unstable even if all individual agents are stable. These results indicate that information processing over networked systems gives rise to some revealing phenomena due to the coupling effect among the agents.