  In dusty (complex) plasmas, containing mesoscopic charged grains, the
grain-grain interaction in many cases can be well described through a Yukawa
potential. In this Review we summarize the basics of the computational and
theoretical approaches capable of describing many-particle Yukawa systems in
the liquid and solid phases and discuss the properties of the dynamical density
and current correlation spectra of three- and two-dimensional strongly coupled
Yukawa systems, generated by molecular dynamics simulations. We show details of
the $\omega(k)$ dispersion relations for the collective excitations in these
systems, as obtained theoretically following the quasilocalized charge
approximation, as well as from the fluctuation spectra created by simulations.
The theoretical and simulation results are also compared with those obtained in
complex plasma experiments.
