  After a succinct review of the MOND paradigm--with its phenomenology, and its
various underlying theories--I concentrate on so called modified inertia (MI)
formulations of MOND, which have so far received only little attention. These
share with all MOND theories the salient MOND predictions, such as
asymptotically flat rotation curves, and the universal mass-asymptotic-speed
relation. My emphasis here is, however, on the fact that MI theories can differ
substantially from their "modified-gravity" (MG) kin in predicting other
phenomena. Because MI theories are non local in time, MOND effects depend on
the full trajectory of a system, not only on its instantaneous state, as in MG
theories. This may lead to rather different predictions for, e.g., the
external-field effect (EFE): A subsystem, such as a globular cluster or a dwarf
galaxy, moving in the field of a mother galaxy, or a galaxy in a cluster, may
be subject to an EFE that depends on the accelerations all along its orbit, not
only on the instantaneous value. And, it is even possible to construct MI
theories with practically no EFE. Other predictions that may differ are also
discussed. Since we do not yet have a full fledged, modified-inertia
formulation, simple, heuristic models have been used to demonstrate these
points.
