  This work discusses quantum states defined in a finite-dimensional Hilbert
space. In particular, after the presentation of some of them and their basic
properties the work concentrates on the group of the quantum optical models
that can be referred to as \textit{quantum optical scissors}. Such "devices"
can generate on their outputs states that are finite-dimensional, and
simultaneously use for such preparation quantum states that are defined in the
infinity-dimensional space. The work concentrates on two groups of models: the
first one, comprising linear elements and the second one -- models for which
optical, Kerr-like nonlinear elements were applied.
