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Because of their non-equilibrium dynamics, active systems can show condensed phases that are prevented by fluctuations at equilibrium. For instance, active particles can condense even in the absence of any attractive force, they can develop collective long-ranged polar order in two spatial dimensions, and they can produce spontaneous currents once embedded into complex environments. In this talk, I will show how most of the peculiarities of active systems can be rationalized in terms of persistent random walks. 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