It is well-established that Patterson-Sullivan measures on the boundary of a hyperbolic space, along with the associated Bowen-Margulis-Sullivan measure, provide valuable insights into the action of a group of isometries on the space's boundary through analysis of the geodesic flow. Given that paths of a random walk on a hyperbolic groups lie close to the group's quasi-geodesics, it is natural to ask whether similar behaviour can also be seen in the flow along bi-infinite random walk paths. In this talk, I will give an insight into classical Patterson-Sullivan theory, and show how studying bi-infinite random walks on a discrete hyperbolic group $G$ leads to an analogue of the Patterson-Sullivan measure on $\partial^2G$. This talk is based on joint work with Mahan Mj and Chiranjib Mukherjee.