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Polydisperse dust, as in astrophysical observations, occurs in a range of sizes, compositions, charges, and masses, with corresponding changes to linear dispersion laws. At the fluid level the charged dust can be treated as a discrete collection of different fluids or as the continuous limit over a charge range. On the other hand, one global dust fluid needs appropriate model equations, derivable from a Klimontovich or extended Vlasov approach, in which charge, mass, and/or size enter as extra phase space variables. Due to differing charge-to-mass weightings, this is sometimes quite involved. An extended kinetic theory allows for a more correct picture, including possible microscopic damping mechanisms, but quickly becomes very unwieldy. An intermediate procedure is to use results for monodisperse dust and integrate afterwards over dust distributions. This cannot be applied blindly, so that it is necessary to check results on their applicability and consistency. Selected applications have been treated for parallel electromagnetic, oblique electrostatic (and possibly self-gravitational), and fluid dust-Bernstein modes, to illustrate the methodological aspects of this part of dusty plasma physics.