Whenever the Seiberg-Witten (SW) invariants of a 4-manifold X are defined, there exist 2-forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubes' "SW=Gr" theorem asserts that the SW invariants are equal to counts of J-holomorphic curves (Taubes' Gromov invariants). In this talk I will describe an extension of Taubes' theorem to non-symplectic X: there are counts of J-holomorphic curves in the complement of these circles, which recover the SW invariants. This "Gromov invariant" interpretation was originally conjectured by Taubes in 1995. This talk will involve ECH and SW-Floer theory.