Recent advances in the study of collective effects and particle motions in plasma-dust crystals are presented. Plasma collective processes influence arrangements and vibrations of dust particles in these Coulomb structures. The important effect is the wake potential formation leading to the vertical alignment of dust grains in the experiments. Oscillations of dust particles in the lattices are strongly affected by collective processes in the ambient plasma, in particular, by the wake. Modes associated with vertical vibrations of dust grains, which can provide a useful tool for diagnostics in the sheath region, are identified, and their dispersion characteristics are discussed.
Low-dimensional structures in a complex cryogenic plasma