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I briefly highlight the salient properties of modified-inertia formulations of MOND, contrasting them with those of modified-gravity formulations, which describe practically all theories propounded to date. Future data (e.g. the establishment of the Pioneer anomaly as a new physics phenomenon) may prefer one of these broad classes of theories over the other. I also outline some possible starting ideas for modified inertia. 1 Modified MOND inertia vs. modified MOND gravity MOND is a modification of non-relativistic dynamics involving an acceleration constant a 0. In the formal limit a 0 → 0 standard Newtonian dynamics is restored. In the deep MOND limit, a 0 → ∞, a 0 and G appear in the combination (Ga 0). Much of the NR phenomenology follows from this simple prescription, including the asymptotic flatness of rotation curves, the mass-velocity relations (baryonic Tully-fisher and Faber Jackson relations), mass discrepancies in LSB galaxies, etc.. There are many realizations (theories) that embody the above dictates, relativistic and non-relativistic. The possibly very significant fact that a 0 ∼ cH 0 ∼ c(Λ/3) 1/2 may hint at the origin of MOND, and is most probably telling us that a. MOND is an effective theory having to do with how the universe at large shapes local dynamics, and b. in a Lorentz universe (with H 0 = 0, Λ = 0) a 0 = 0 and standard dynamics holds. We can broadly classify modified theories into two classes (with the boundary not so sharply defined): In modified-gravity (MG) formulations the field equation of the gravitational field (potential, metric) is modified; the equations of motion of other degrees of freedom (DoF) in the field are not. In modified-inertia (MI) theories the opposite it true. More precisely, in theories derived from an action modifying inertia is tantamount to modifying the kinetic (free) actions of the non-gravitational degrees of freedom. Local, relativistic theories in which the kinetic