We show that shot noise is an informative tool for studies of hopping and resonant tunnelling between localized electron states. In hopping via several states, shot noise is seen to be always suppressed compared with its classical Poisson value SI = 2eI (I is the average current). The degree of suppression depends on the geometry of current paths and the distribution of the barriers between the localized states. In resonant tunnelling through a single impurity an unusual enhancement of shot noise is observed. It has been established, both experimentally and theoretically, that a considerable increase of noise occurs in the case of two interacting resonant tunnelling channels.