  A review on the properties and dynamical origin and nature of the cosmic
foam, the tenuous space-filling frothy network permeating the interior of the
Universe. We discuss the properties of this striking and intriguing pattern,
describing its observational appearance, and seeking to elucidate its dynamical
origin and nature. An extensive discussion on the gravitational formation and
dynamical evolution of weblike patterns puts particular emphasis on the
formative role of the generic anisotropy of the cosmic gravitational force
fields. These tidal fields play an essential role in shaping the pattern of the
large scale cosmic matter distribution. Special attention is put on a
geometrical and stochastic framework for a systematic evaluation of its fossil
information content on the cosmic structure formation process. Its distinct
geometric character and the stochastic nature provides the cosmic web with some
unique and at first unexpected properties. The implications for galaxy
clustering are discussed on the basis of its relevant branch of mathematics,
stochastic geometry. Central within this context are Voronoi tessellations,
which have been found to represent a surprisingly versatile model for spatial
cellular distributions.
