The universe is largely observed with electromagnetic signals - supposedly Maxwellian - though the gravitational wave window was just unbarred. Meanwhile, cosmology is since long confronted with an universe for 96% dark and unknown. Thus, it is pertinent for fundamental physics to start a theoretical and experimental verification of electromagnetism, and its photon messenger. The study discusses nonMaxwellian theories, focusing on testable effects. We deal with a range of applications and assess how alternative electromagnetic theories are helpful. We revise the most notable theories, either...