Dusty plasmas are ubiquitous in low-temperature laboratory discharges as well as in the near-earth environment, planetary rings, and interstellar spaces. In this paper, updated knowledge of fundamentals of collective dust-plasma interactions and several novel phenomena are presented that have been observed in laboratories and in space dusty plasmas. Mechanisms that are responsible for the charging of dust grains are discussed, and the fact that the dust charge perturbation is a new dynamical variable in a dusty plasma. The underlying physics of different forces that act on a charged dust grain is reviewed. In dusty plasmas, there are new attractive forces (e.g., due to wakefield and ion focusing effects and dipole-dipole interactions between unevenly charged dust rods). Furthermore, in the presence of an ensemble of charged dust grains, there are collective dust-plasma interactions featuring new waves (e.g., the dust acoustic wave, the dust ion-acoustic wave, the dust lattice wave, etc.), new instabilities, and coherent nonlinear structures (dust acoustic and dust ion-acoustic shocks, dust voids, and dust vortices), which are also discussed. Theoretical models for numerous collective dust-plasma interactions are compared with existing observations from laboratories and space environments.

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects, in semiconductors and micro-mechanical systems, as well as in the next generation intense laser-solid density plasma interaction experiments and in quantum x-ray free-electron lasers. In contrast to classical plasmas, one encounters extremely high plasma number density and low temperature in quantum plasmas. The latter are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, holes) follow the Fermi-Dirac statistics. In quantum plasmas, there are new forces associated with i) quantum statistical electron and positron pressures, ii) electron and positron tunneling through the Bohm potential, and iii) electron and positron angular momentum spin. Inclusion of these quantum forces provides possibility of very high-frequency dispersive electrostatic and electromagnetic waves (e.g. in the hard x-ray and gamma rays regimes) having extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave-wave and wave-electron interactions in dense quantum plasmas. Specifically, we shall focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of 3D quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase space kinetic structures and mechanisms that can generate quasi-stationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed.

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, model equations (e.g., the quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations) are presented 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 wave functions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2 quantum particles), 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, nonlinear features of ES ion waves and electron plasma oscillations are discussed, as well as the trapping of intense EM waves in quantum electron-density cavities. Specifically, simulation studies of the coupled nonlinear Schr\"odinger and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. The effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic equations are also discussed. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets), as well as in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, nanophotonics and nanoplasmonics, metallic nanostructures, thin metal films, semiconductor quantum wells, and quantum dots, etc.), and in the next generation of intense laser-solid density plasma interaction experiments relevant for fast ignition in inertial confinement fusion schemes.

We present simulation studies of the formation and dynamics of dark solitons and vortices in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson system of equations, which conserves the number of electrons as well as their momentum and energy. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear structures presented here may serve the purpose of transporting information at quantum scales in ultracold micromechanical systems and dense plasmas, such as those created during intense laser-matter interactions.