  Understanding the electron dynamics and transport in metallic and
semiconductor nanostructures -- such as metallic nanoparticles, thin films,
quantum wells and quantum dots -- represents a considerable challenge for
today's condensed matter physics, both fundamental and applied. In this review
article, we will describe the collective electron dynamics in metallic and
semiconductor nanostructures using different, but complementary, approaches.
For small excitations (linear regime), the spectral properties can be
investigated via quantum mean-field models of the TDLDA type (time-dependent
local density approximation), generalized to account for a finite electron
temperature. In order to explore the nonlinear regime (strong excitations), we
will adopt a phase-space approach that relies on the resolution of kinetic
equations in the classical phase space (Vlasov and Wigner equations). The
phase-space approach provides a useful link between the classical and quantum
dynamics and is well suited to model effects beyond the mean field
approximation (electron-electron and electron-phonon collisions). We will also
develop a quantum hydrodynamic model, based on velocity moments of the
corresponding Wigner distribution function: this approach should lead to
considerable gains in computing time in comparison with simulations based on
conventional methods, such as density functional theory (DFT). Finally, the
magnetization (spin) dynamics will also be addressed.
