  This short review presents a few case studies of finite electron systems for
which strong correlations play a dominant role. In simple metal clusters, the
valence electrons determine stability and shape of the clusters. The ionic
skeleton of alkali metals is soft, and cluster geometries are often solely
determined by electron correlations. In quantum dots and rings, the electrons
may be confined by an external electrostatic potential, formed by a gated
heterostructure. In the low density limit, the electrons may form so-called
Wigner molecules, for which the many-body quantum spectra reveal the classical
vibration modes. High rotational states increase the tendency for the electrons
to localize. At low angular momenta, the electrons may form a quantum Hall
liquid with vortices. In this case, the vortices act as quasi-particles with
long-range effective interactions that localize in a vortex molecule, in much
analogy to the electron localization at strong rotation.
