Networked systems control is a known problem complicated because of the need to work with large groups of elementary agents. In many applications, it is impossible (or difficult) to validate agent movement models and provide sufficiently reliable control actions at the elementary system components level. The evolution of agent subgroups (clusters) leads to additional uncertainty in the studied control systems. We focus on new decentralized control methods based on local communications in complex multiagent dynamical systems. The problem of intelligence in a complex world is considered in connection to multiagent network systems, including a system named airplane with feathers, load balancing, and the multisensor-multitarget tracking problem. Moreover, the new result concerning the emergency of intelligence in a group of robots is provided. All these methods follow the paradigm of the direct reaction of each element (agent) of the system to its sensory data of current situation observations and the corresponding data from a limited number of its neighbors (local communications). At the same time, these algorithms achieve a mutual goal at the macro level. All of the considered emergent intelligence appearances inspire the necessity to "rethink" the previously recognized concepts of computability and algorithm in computer science.