Mobile robots that communicate and cooperate to achieve a common task have been the subject of an increasing research interest in recent years. These possibly heterogeneous groups of robots communicate locally via a communication network and therefore are usually referred to as robotic networks. Their potential applications are diverse and encompass monitoring, exploration, search and rescue, and disaster relief. From a research standpoint, in this thesis we consider specific aspects related to the foundations of robotic network algorithmic development: distributed estimation, control, and optimization. The word “distributed” refers to situations in which the cooperating robots have a limited, local knowledge of the environment and of the group, as opposed to a “centralized” scenario, where all the robots have access to the complete information. The typical challenge in distributed systems is to achieve similar results (in terms of performance of the estimation, control, or optimization task) with respect to a centralized system without extensive communication among the cooperating robots. In this thesis we develop effective distributed estimation, control, and optimization algorithms tailored to the distributed nature of robotic networks. These algorithms strive for limiting the local communication among the mobile robots, in order to be applicable in practical situations. In particular, we focus on issues related to nonlinearities of the dynamical model of the robots and their sensors, to the connectivity of the communication graph through which the robots interact, and to fast feasible solutions for the common (estimation or control) objective.