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Mobile robot networks emerged in the past few years as a promising distributed computing model. Existing work in the literature typically ensures the correctness of mobile robot protocols via ad hoc handwritten proofs, which are both cumbersome and error-prone. This paper surveys state-of-the-art results about applying formal methods approaches (namely, model-checking, program synthesis, and proof assistants) to the context of mobile robot networks. Those methods already proved useful for bug-hunting in published literature, designing correct-bydesign optimal protocols, and certifying impossibility results. We also present related open questions to further develop this path of research.