Numerical Star-Formation Studies -- A Status Report
  The formation of stars is a key process in astrophysics. Detailed knowledge
of the physical mechanisms that govern stellar birth is a prerequisite for
understanding the formation and evolution of our galactic home, the Milky Way.
A theory of star formation is an essential part of any model for the origin of
our solar system and of planets around other stars. Despite this pivotal
importance, and despite many decades of research, our understanding of the
processes that initiate and regulate star formation is still limited.
  Stars are born in cold interstellar clouds of molecular hydrogen gas. Star
formation in these clouds is governed by the complex interplay between the
gravitational attraction in the gas and agents such as turbulence, magnetic
fields, radiation and thermal pressure that resist compression. The competition
between these processes determines both the locations at which young stars form
and how much mass they ultimately accrete. It plays out over many orders of
magnitude in space and time, ranging from galactic to stellar scales. In
addition, star formation is a highly stochastic process in which rare and
hard-to-predict events, such as the formation of very massive stars and the
resulting feedback, can play a dominant role in determining the evolution of a
star-forming cloud.
  As a consequence of the wide range of scales and processes that control star
formation, analytic models are usually restricted to highly idealized cases.
These can yield insight, but the complexity of the problem means that they must
be used in concert with large-scale numerical simulations. Here we summarize
the state of modern star formation theory and review the recent advances in
numerical simulation techniques.
