The main topics of this thesis are distributed estimation and cooperative path-following in the presence of communication constraints, with applications to autonomous marine vehicles. To this end, we study algorithms that take explicitly into account the constraints imposed by the communication channel, either by reducing the total number of messages per unit of time or quantizing the information with a reduced number of bits and transmitting it at a fixed rate. We develop a cooperative path following (CPF) algorithm with event-triggered communications and show both through simulations and sea trials with Medusa-class marine vehicles that the self-triggered cooperative path-following algorithm proposed yields adequate performance for formation control of autonomous marine vehicles, while reducing substantially the communications among the vehicles. By exploiting tools from quantized consensus theory, we also provide a method for cooperative path-following with quantized communications, and an algorithm for distributed estimation and control with quantized communications. The performance of the resulting systems is illustrated in simulations. A new methodology for the design of distributed estimators for linear systems is proposed that yields guaranteed stability in the case of collectively observable systems. The resulting algorithm only requires the broadcasting of each node’s state estimate at each discrete time instant. We show via simulations that for some particular conditions the algorithm has a lower estimation error norm than other methods that use the same bandwidth and yields stable estimation errors for unstable systems. This thesis also proposes a distributed estimation and control algorithm with progressive quantization. We show that with an appropriate parameter choice and given that the system is collective detectable, the algorithm proposed yields a bounded estimation error and state for every agent, with bounds proportional to the process and measurement noise of the system. Finally, it is shown in tests with model cars that distributed estimation with quantized consensus is a feasible strategy for formation control using only range measurements between the vehicles.