We are focused on these three areas: (1) A new Lorentz-covariant nonlinear extension of classical electrodynamics was proposed. It uses only the electromagnetic degrees of freedom – Strong-Field Electrodynamics. This allowed us to calculate the first dissipative pulsar magnetosphere. (2) With Farrar, we proposed that ultra-high-energy cosmic rays can come from rare bright flares on supermassive black holes. (3) A new scenario for magnetic field generation in the cosmic plasma was described.