Abstract A qualitative discussion of the essentials of small-polaron motion is presented. After a very brief description of the notion of a small polaron and the situation under which it is formed, the principal physical features and predictions of the theory of small-polaron transport is addressed. Specifically, small-polaron band and hopping motion are both initially considered with the discussion thereafter being restricted to hopping motion. First quantum-mechanical treatments of small-polaron hopping motion are considered. Then the semiclassical approach to the calculation of the high-temperature (κT ≳ħω Debye) adiabatic and nonadiabatic jump rate is described with the question of correlated hopping motion also being addressed. After this, the high-frequency absorption associated with small-polaron motion is considered. Finally, a review of the Hall-mobility calculations and some comments about the thermoelectric power are presented.