The development of classical and quantum electrodynamics were highlights of nineteenth and twentieth century physics, respectively. Observations of neutron stars and black holes are taking these disciplines into new and extreme territory. We are observing magnetic field of strength greater than 100 GT, potential differences more than 1 ZV, effective temperatures above 10^40 K, neutrinos and gamma rays with energy more than 1 PeV and 300 EeV cosmic rays. The Simons Collaboration that is addressing these challenges will be introduced and some recent research on the acceleration of Ultra High Energy Cosmic Rays, the interpretation of the EHT image of the black hole in M87 and the origin of Fast Radio Bursts will be outlined.