MOND--particularly as modified inertia
  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. 
Mordehai Milgrom
astro-ph.CO gr-qc hep-ph