Dusty plasma consisting of electrons, ions, and charged dust grains may exist in space and astrophysical environments as well as in the laboratory. This paper presents an overview of the characteristics of hydromagnetic waves propagating in a magnetized dusty plasma. Two physical models are considered: ion and dust Hall magnetohydrodynamic models describing the properties of hydromagnetic waves with ion and dust inertial frequencies, respectively. The dispersion relations and magnetic field polarizations as well as the density-magnetic field relations are derived. It is shown that due to the presence of massive charged dust grains it is possible to have whistler and cyclotron waves with left-handed and right-handed magnetic polarizations, respectively, which is in contrast to the usual electron-ion plasmas.