  In this review, an overview of structural properties and phase transitions in
finite spherical dusty (complex) plasma crystals -- so-called Yukawa balls --
is given. These novel kinds of Wigner crystals can be directly analyzed
experimentally with video cameras. The experiments clearly reveal a shell
structure and allow to determine the shell populations, to observe metastable
states and transitions between configurations as well as phase transitions. The
experimental observations of the static properties are well explained by a
rather simple theoretical model which treats the dust particles as being
confined by a parabolic potential and interacting via an isotropic Yukawa pair
potential. The excitation properties of the Yukawa balls such as normal modes
and the dynamic behavior, including the time-dependent formation of the crystal
requires, in addition, to include the effect of friction between the dust
particles and the neutral gas. Aside from first-principle molecular dynamics
and Monte Carlo simulations several analytical approaches are reviewed which
include shell models and a continuum theory. A summary of recent results and
theory-experiment comparisons is given and questions for future research
activities are outlined.
