Quantum communication has been the most successful aspect of quantum computation in terms of applications and physical implementations. We focus on aspects that have direct impact on the overarching objectives of this proposal. Communication complexity is an indispensable tool for analysing informational bottlenecks in computation. As a transversal theme, we study channel capacities in networks, where our main goal is to establish trade-offs between noise and achievable transmission rates that are practically useful. Finally, we will study how susceptible classical cryptosystems are to quantum attacks.