  In this paper a comprehensive review is given on the current status of
achievements in the geometric aspects of the Painlev\'e equations, with a
particular emphasis on the discrete Painlev\'e equations. The theory is
controlled by the geometry of certain rational surfaces called the spaces of
initial values, which are characterized by eight point configuration on
$\mathbb{P}^1\times\mathbb{P}^1$ and classified according to the degeration of
points. We give a systematic description of the equations and their various
properties, such as affine Weyl group symmetries, hypergeomtric solutions and
Lax pairs under this framework, by using the language of Picard lattice and
root systems. We also provide with a collection of basic data; equations, point
configurations/root data, Weyl group representations, Lax pairs, and
hypergeometric solutions of all possible cases.
