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https://doi.org/10.1007/978-1-84800-324-8This chapter is a brief presentation of the randomly biased random walk on trees in its slow regime. The model has been introduced by Lyons and Pemantle (Ann Probab 20:125–136, 1992), as an extension of Lyons’s deterministically biased random walk on trees (Lyons, Ann Probab 18:931–958, 1990; Lyons, Ann Probab 20:2043–2088, 1992).