When the mean-free path length of conduction electrons in a metal $l^\infty$ is comparable to the thickness of the specimen $d$, various kinds of size effects appear. To study these effects, under the cleanest conditions, filamentary crystals--whiskers--are used. At low temperatures conditions under which $l^\infty\gg d$ are easily achieved in whiskers. In this case the interaction of electrons with the surface is determining, and this markedly changes the electronic properties characteristic for the usual massive $(d\gg l^\infty)$ specimens. In this review the results of the experimental study of the effect of dimensions on the electrical resistance of whiskers, permitting the determination of the degree of specularity of the reflection of electrons from the surface, are examined. In a magnetic field under the condition that $l^\infty\gg d$, $r$ the theory predicted new phenomena: a dc skin-effect confined to a thin (of the order of the Larmor radius $r$) surface layer of the specimen, a change in the quantum effects for $r>d$, as well as other effects. Experiments on whiskers in which these phenomena are observed are described in this review. Experiments in which the high (close to the theoretical limit) strength of whiskers is used to investigate electronic 2.5-order transitions are also described.