Once contact is made with an extraterrestrial intelligence, we will want to move rapidly beyond the expected exchange of mathematical concepts to an investigation of their civilization. This might best be done by learning one another’s language(s). This paper discusses the nature of Earth’s 7,000 languages to see what they have in common, what they lack and what this might reveal about human thought. It also offers hypotheses about the structure and learnability of languages that might evolve on other planets. Methods for learning and teaching language would depend partly on the medium of communication: the (more likely) exchange of information asynchronously at a distance would be very different from or the (much less likely) ‘Arrival-style’ monolingual field methods approach. In either case, xenolinguists would have to sustain dozens of simultaneous linguistic hypotheses and be ready to work with high rates of error.