During the last decade, we have seen a very rapid growth of the dusty plasma physics with many discoveries. The latter include the dust acoustic wave, the wakefield and the ion focusing (which are responsible for the attraction of charged dust grains), the dusty plasma crystals as well as coherent nonlinear structures comprising the dust ion-acoustic shocks, the dust acoustic Mach cones, voids, and vortices. Since the dusty plasma physics involves the charging and the dynamics of extremely massive charged dust grains, it can be characterized as a complex plasma system whose characteristics are significantly different from the usual multi-ion plasmas. In this paper, we present the properties of a complex dusty plasma, as well as discuss two novel instabilities that are responsible for the excitation of low-frequency electrostatic modes in an unmagnetized dusty plasmas. The instabilities are associated with the combined effects of a dc electric field and the dust charge gradient on one hand, and the rotation of elongated dust grains on the other hand. The implications of the present investigation to laboratory and space plasmas are discussed. ©2000 American Institute of Physics.