The Poisson boundary of a countable group G endowed with a probability measure ? is a probability space that encodes all bounded ?-harmonic functions on G. Alternatively, it captures the asymptotic directions of the ?-random walk on G. A natural problem is to identify an explicit model of the associated Poisson boundary, described in terms of the geometry of the group G. I will discuss the identification problem of Poisson boundaries for random walks with finite entropy on Baumslag-Solitar groups. Our results are expressed in terms of both the action of a Baumslag-Solitar group on its Bass-Serre tree and the action by affine transformations on the rational numbers Q. These results generalize the work of Kaimanovich and Cuno-Sava-Huss to a setting where no conditions are imposed on the moments of the measures.This is joint work with Kunal Chawla.