Dust is ubiquitous in the universe and responsible for stellar and planetary formation. Virtually all previous studies have considered the dust particulates to be a charge neutral component. Satellite missions such as Voyager revealed the extent to which charged dust plays a role in astrophysics. In most areas dust exists in the presence of a dilute plasma. In such a plasma environment the dust becomes charged to a variety of processes (eg photo-ionisation, collisions with electrons and ions, thermionic emission etc). Closer to home in the Earth's mesosphere, rocket measurements and radar observations conclusively demonstrate the importance of charged dust in forming complex structures responsible for Polar Mesospheric Summer Echoes. This book is the outcome of a periodic collaboration between a small group of scientists meeting twice a year at the International Space Science Institute (ISSI) in Bern, Switzerland over a period of three years. The book begins with a description of the fundamental physical processes which characterise dusty plasmas. Starting with charging and shielding of isolated dust particles in a plasma environment, the review progresses to non-linear dust dynamics of spherical and irregular dust. In an ensemble of a dust plasma system collective processes begin to manifest themselves in the form of new wave modes and instabilities which play an important role in the collective behaviour displayed in space and astrophysical environment. Finally more exotic topics, such as the Ising model for irregular dust grain alignment, classical Casimir forces and chargeons are explored.