Relativistic jets transport energy from near a galaxy’s central supermassive black hole to extragalactic distances. The leading theory of jet launching is the Blandford–Znajek (BZ) mechanism, in which magnetic fields threading the event horizon extract the black hole’s spin energy. However, black hole energy extraction has never been confirmed observationally. In this talk, I will show how Event Horizon Telescope (EHT) images of the black holes M87* and Sgr A* are providing our first direct measurements of jet-launching magnetic fields on event-horizon scales. These polarimetric images strongly suggest that the accretion flows in both sources are in the magnetically arrested state. In this state, coherent magnetic fields threading the event horizon become strong enough to push back on infalling gas. Analytic models and simulations show that the handedness of the polarization spiral in EHT images directly probes the direction of electromagnetic energy flux near the black hole. The observed polarization in M87* suggests that energy flows outward near the horizon, but the polarization’s year-to-year variability is difficult to explain with theoretical models. If energy flows outward from Sgr A*, its resolved polarization indicates that it spins clockwise on the sky, consistent with near-infrared flare observations. Finally, I will show that the polarization of synchrotron radiation from black holes with axisymmetric magnetic fields has a universal limit set by strong frame dragging as the emission approaches the horizon; its limiting direction depends only on the black hole spin and inclination. Future EHT and space-based interferometry experiments will probe these horizon-threading magnetic fields and enable a direct test of the BZ mechanism for powering extragalactic jets.