How come photons have no mass if they have energy and $E=mc^2$?

Question

If photons have no mass, and yet have energy, how is that compatible with $E=mc^2$? Anything having mass should have energy (and the opposite should be true as well no)?

Answer 1

$E=mc^2$ is a statement about energy in the rest frame. The photon rest frame does not exist but one can approach it in principle by moving along with a photon at near light speed. The photon will be red shifted and its energy will approach zero. In this limit $E=mc^2=0$.