Abstract: In 2017, Braverman-Finkelberg-Nakajima gave a precise definition of the Coulomb branch of a 3d N = 4 supersymmetric gauge theory of cotangent type associated to a complex reductive group G and a finite dimensional complex representation N. In our first part of this talk, we will recall the definition and basic properties of such Coulomb branches, as well as give some motivation for its study. We will then discuss an alternate definition of the Coulomb branch for (G, N) due to Teleman assuming that (G, N) satisfies a certain condition that we call gluable. In the second part of this talk, we will discuss functoriality of these Coulomb branches: in other words, we will discuss how, given a map of reductive groups H –> G, one can recover the Coulomb branch associated to the pair (H, N) from the pair (G, N), assuming our map is gluable. We will also discuss the connections to functoriality in the geometric Langlands program and explain our conjecture, recently proved by Victor Ginzburg, that the Coulomb branch of (G, N) determines the S-dual (in the sense of, say, Ben-Zvi–Sakellaridis–Venkatesh) of the pair (G, N). This is joint with Ben Webster.