Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social, man-made and biological networks. We find that human networks of governance and collaboration have predictable communication on tête-à-tête level, reflecting well-defined pathways. In contrast, communication pathways in the Internet are more distributed. For molecular networks, the communication ability in the single-celled yeast resembles the one of human networks, whereas the more complicated Drosophila is closer to the Internet. For all investigated networks, the global communication is worse than for their random counterparts, reflecting the fact that long-distance communication is disfavored.