  This is a critical review of inert properties of classical relativistic point
objects. The objects are classified as Galilean and non-Galilean. Three types
of non-Galilean objects are considered: spinning, rigid, and dressed particles.
In the absence of external forces, such particles are capable of executing not
only uniform motions along straight lines but also Zitterbewegungs,
self-accelerations, self-decelerations, and uniformly accelerated motions. A
free non-Galilean object possesses the four-velocity and the four-momentum
which are in general not collinear, therefore, its inert properties are
specified by two, rather than one, invariant quantities. It is shown that a
spinning particle need not be a non-Galilean object. The necessity of a rigid
mechanics for the construction of a consistent classical electrodynamics in
spacetimes of dimension D+1 is justified for D+1>4. The problem of how much the
form of fundamental laws of physics orders four dimensions of our world is
revised together with its solution suggested by Ehrenfest. The present analysis
made it apparent that the notion of the ``back-reaction'' does not reflect the
heart of the matter in classical field theories with point-like sources, the
notion of ``dressed'' particles proves more appropriate.
