  The present review is devoted to the problems of finite-size scaling due to
the presence of long-range interaction decaying at large distance as
$1/r^{d+\sigma}$, $\sigma>0$. The attention is focused mainly on the
renormalization group results in the framework of ${\cal O}(n)$ $\phi^{4}$ -
theory for systems with fully finite (block) geometry under periodic boundary
conditions. Some bulk critical properties and Monte Carlo results also are
reviewed. The role of the cutoff effects as well their relation with those
originating from the long-range interaction is also discussed. Special
attention is paid to the description of the adequate mathematical technique
that allows to treat the long-range and short-range interactions on equal
ground. The review closes with short discussion of some open problems.
