The propagation of ultra low-frequency electrostatic modes in dusty plasmas has been reviewed in the light of the concept of dust fugacity (f&hthinsp;), which is defined byf≡4&pgr;nd0&lgr;D2Rwherend0,&lgr;DandRare, respectively, the dust number density, the plasma Debye length and the grain size (radius). Dusty plasmas are defined to be tenuous, dilute or dense according asf≪1,∼1, or ≫1, respectively. By using the fluid as well as the kinetic (Vlasov) theories, attention is focused on the “Dust-Acoustic Waves” (DAWs) and the “Dust-Coulomb Waves” (DCWs) which exist in the tenuous and the dense regimes, respectively. Unlike the DAWs which exist even for constant grain charge, the DCWs are thenormal modesassociated with grain charge fluctuations, and are driven by an effective pressure called “Coulomb Pressure”. They can be considered as the electrostatic analogue of the hydromagnetic (Alfve´n or magnetoacoustic) modes which are driven by the magnetic field pressure. In the dilute regime, the two modes merge into a single mode, which may be called the “Dust Charge-Density Wave” (DCDW). When the grains are closest, the DCW dispersion relation is identical with that of the “Dust-Lattice Waves” (DLWs). Dense dusty plasmas are shown to be governed by anew scale-lengthdefined by&lgr;R≡1/4&pgr;nd0R&dgr;,where &dgr; is a parameter related to the charging frequencies. The scale-length&lgr;Rcharacterizes the effective shielding length due to the collective grain interactions, and plays a fundamental role in dense dusty plasmas, which is very similar to that of the Debye length(&lgr;D)of the tenuous regime. The frequency spectrum as well as the damping rates for the various dust modes have been analytically obtained, and compared with the numerical results. ©2000 American Institute of Physics.