Mass is Energy:
The consequences of E=mc²

It was, of course, the realization that mass and energy are equivalent that led to the development of the atom bomb, but there are far more important consequences of this most famous equation than its destructive power. Actually, new insights into this equation have led to a radically different idea of mass itself: conceptually speaking, it simply isn't necessary. Einstein's theory, it has been suggested, merely tells how much energy is needed to give the appearance of a certain amount of mass. There is no mass, only electric charge and energy.

Inertia, under this interpretation, would arise from the presence of a Zero Point Field (ZPF), which is speculated to be an electromagnetic filed that exists everywhere in space. For an explanation of why physicists have theorized an aether-like ubiquitous substance, and what it actually means, see the article Beyond E=mc²; I don't pretend to understand it fully, so it would be better to read about it from the people who do.