  Practically all the full-fledged MOND theories propounded to date are of the
modified-gravity (MG) type: they modify only the Newtonian, Poisson action of
the gravitational potential, or the general-relativistic Einstein-Hilbert
action, leaving other terms (inertia) intact. Here, I discuss the
interpretation of MOND as modified inertia (MI). My main aim is threefold: (a)
to advocate exploring MOND theories beyond MG, and appreciating their
idiosyncrasies, (b) to highlight the fact that secondary predictions of such
theories can differ materially from those of MG theories, (c) to demonstrate
some of this with specific MI models. I discuss some definitions and
generalities concerning MI. I then present instances of MI in physics, and the
lessons we can learn from them for MOND. I then concentrate on a specific class
of nonrelativistic, MOND, MI models, and contrast their predictions with those
of the two workhorse, MG theories -- AQUAL and QUMOND. The MI models predict
possibly a stronger external-field effect -- e.g. on low acceleration systems
in the solar neighborhood -- such as very wide binary stars -- and on vertical
motions in disc galaxies. More generally, the workings of the effect are rather
different, and depend in different ways on dimensionless characteristics of the
system, such as frequency ratios of the external and internal fields,
eccentricity of trajectories, etc. These models predict a {\it much} weaker
effect of the Galactic field in the inner Solar System than is predicted by
AQUAL/QUMOND. I also show how noncircular motions -- such as those
perpendicular to the disc -- modify the standard, algebraic
mass-discrepancy-acceleration relation (aka RAR) that is predicted by MI for
exactly circular orbits. These differences, and more that are discussed, can
potentially offer ways to distinguish between theories.
