The subject of this talk will be quantum distributed computing, i.e., distributed computing when the processors of the network can exchange quantum information. After describing the basics of distributed computing, I will explain a result obtained with Frédéric Magniez (arXiv:1804.02917) on quantum algorithms computing the diameter of the network. I will then present others results (arXiv:1810.10838 and arXiv:1908.11488) that show separations between the computational powers of quantum and classical distributed algorithms in several fundamental models of distributed computing. I will conclude my talk by mentioning interesting and important open questions in quantum distributed computing.