Abstract: Perverse schobers refer to perverse sheaves of (enhanced) triangulated categories, as introduced by Kapranov-Schechtman. Though their general theory remains conjectural, there exists a robust theory of perverse schobers on surfaces with boundary. In the talk, we will discuss how such perverse schobers naturally arise from cosheaves of Fukaya categories of Lefschetz fibrations constructed by Ganatra-Pardon-Shende. For instance, in the case of the disc, the Fukaya-Seidel category arises as the category of global sections of a perverse schober. We then discuss how the formalism of perverse schobers can facilitate many computations. A key point is that by using sheaves of categories, as opposed to cosheaves, one can construct objects and morphisms in the global category via the gluing of local data. Finally, we will also indicate examples of perverse schobers in higher dimensions arising from repeated Lefschetz fibrations (obtained in joint work with Dyckerhoff and Walde).