We give an introduction to 3D mirror symmetry directed towards symplectic geometers. Our main focus will be "symplectic C^* manifolds", introduced by Alexander Ritter and Filip Zivanovic in their recent papers. We will give examples and explicit computations that illustrates the main difficulties that arise for these manifolds. If time permits, we will also try to introduce the holomorphic Fueter equations, which can be interpreted as the quaternionic analogue of the J-holomorphic equations.