The ability to cooperate through language is a defining feature of humans. As the perceptual, motory and planning capabilities of deep artificial networks increase, researchers are studying whether they also can develop a shared language to interact. In this talk, I will highlight recent advances in this field but also common headaches (or perhaps limitations) with respect to experimental setup and evaluation of emergent communication. Towards making multi-agent communication a building block of human-centric AI, and by drawing from my own recent work, I will discuss approaches on making emergent communication relevant for human-agent communication in natural language.