Traditional plasma physics has mainly focused on regimes characterized by high temperatures and low densities, for which quantum-mechanical effects have virtually no impact. However, recent technological achievements (particularly on miniaturized semiconductor devices and nanoscale objects) have made it possible to envisage practical applications of plasma physics where the quantum nature of the charged particles plays a crucial role. In this paper, I shall review different approaches to the problem of modeling quantum effects in electrostatic collisionless plasmas. The full kinetic model is in principle given by the Wigner equation, which is the quantum analog of the classical Vlasov equation. The Wigner formalism is particularly attractive, as it recasts quantum mechanics in the familiar classical phase space. However, this is at the cost of having to deal with distribution functions that can take negative values. Equivalently, the Wigner model can be expressed in terms of N one-particle Schrdinger equations, coupled by Poissons equation: this is the Hartree formalism, which is also the quantum analog of the multi-stream approach, wellknown in plasma physics since the works of John Dawson in the sixties. In order to reduce the complexity of the above approaches, it is possible to develop a quantum fluid model by taking velocity-space moments, as is usually done for classical plasmas. Interestingly, this quantum fluid model can be recast as a single nonlinear Schrdinger equation. Finally, certain regimes (particularly at large excitation energies) can be described by semiclassical kinetic models (Vlasov-Poisson), provided that the initial ground-state equilibrium is treated quantum-mechanically using a Fermi-Dirac distribution. Practical applications of the above results to the physics of metal clusters, nanoparticles and thin metal films will be illustrated.