The dusty plasma is a system that consists of many strongly-charged fine dust particles suspended in a plasma background. The slow dynamics and strong coupling due to the large mass and charges lead to the formation of highly-ordered dust crystal structures suspended in the plasma background, which can be directly observed. The dusty plasma forms a link to the area of condensed matter physics for the study of many interesting microscopic phenomena from order to disorder. In this paper, we introduce the special properties of this system from the viewpoint of conventional plasma physics, then we briefly review past works on the structure and dynamical behaviour from the highly-ordered state, through the melting and liquid states with associated vortex-type excitation and anomalous diffusion, to the state with self-organized macroscopic dust waves after losing microscopic order. The first observation of strongly-coupled dust Coulomb clusters with small numbers of particles from a few to a few hundred, which resemble classical atoms, is also demonstrated.