  With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds,
compact and non-compact, smooth and singular. Emphasis will be placed on the
algorithms and databases which have been established over the years, and how
they have been useful in the interaction between the physics and the
mathematics, especially in string and gauge theories. A skein which runs
through this review will be algorithmic and computational algebraic geometry
and how, implementing its principles on powerful computers and experimenting
with the vast mathematical data, new physics can be learnt. It is hoped that
this inter-disciplinary glimpse will be of some use to the beginning student.
