In this talk, I will summarize recent progress in the understanding of 4d effective field theories (EFTs), with a particular eye towards EFT extensions of the Standard Model. The first three pieces illustrate how helicity selection rules govern many surprising properties of the Standard Model EFT at one loop and beyond, including vanishing one-loop helicity amplitudes; vanishing two-loop anomalous dimensions; and vanishing one-loop Wilson coefficients that have been characterized elsewhere as violations of Wilsonian naturalness. Taken together, they reveal a rich and surprising quantum structure of 4d EFTs quite unlike that of their renormalizable counterparts. The remaining pieces survey recently-developed geometric methods for EFTs of the Higgs sector, including a new understanding of the connection between EFT geometry and observables; a new notion of `functional geometry’ invariant under derivative field redefinitions; and a new off-shell recursion relation for EFT amplitudes that follows from this functional geometry. These developments sharpen an open question to address at the LHC and future colliders: is electroweak symmetry linearly realized by the known particles of the Standard Model?