The Betti geometric Langlands program purports to give a conjectural equivalence between two 4-dimensional topological field theories. In its most optimistic formulation, these field theories are fully extended and thus determined by their respective 3-categories of boundary conditions. This formulation remains out of reach due to difficulties in defining the relevant 3-categories (particularly on the A-side); nevertheless, by judicious compactifications of these theories, we can produce rigorous mathematical conjectures, including predictions of the so-called relative Langlands program. We will describe this philosophy, which has been developed by many authors over the last decade and a half, and review and recent mathematical progress, especially from the lens of "homological 3d mirror symmetry" developed in joint work with J. Hilburn & with Hilburn--Mazel-Gee.