  The current understanding of some important nonlinear collective processes in
quantum plasmas with degenerate electrons is presented. After reviewing the
basic properties of quantum plasmas, we present model equations (e.g. the
quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations)
that describe collective nonlinear phenomena at nanoscales. The effects of the
electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's
exclusion principle for overlapping electron wavefunctions that result in
tunneling of electrons and the electron degeneracy pressure. Since electrons
are Fermions (spin-1/2), there also appears an electron spin current and a spin
force acting on electrons due to the Bohr magnetization. The quantum effects
produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a
quantum plasma that are summarized in here. Furthermore, we discuss nonlinear
features of ES ion waves and electron plasma oscillations (ESOs), as well as
the trapping of intense EM waves in quantum electron density cavities.
Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS)
and Poisson equations reveal the formation and dynamics of localized ES
structures at nanoscales in a quantum plasma. We also discuss the effect of an
external magnetic field on the plasma wave spectra and develop quantum
magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding
numerous collective phenomena in quantum plasmas, such as those in compact
astrophysical objects, in plasma-assisted nanotechnology, and in the
next-generation of intense laser-solid density plasma interaction experiments.
