  Based on the formulation of Yang-Baxter sigma models developed by Klimcik and
Delduc-Magro-Vicedo, we explain that various deformations of type IIB
superstring on AdS$_5\times$S$^5$ can be characterized by classical
$r$-matrices satisfying the classical Yang-Baxter equation (CYBE). The relation
may be referred to as `the gravity/CYBE correspondence.' We present non-trivial
examples of the correspondence including Lunin-Maldacena backgrounds for
$\beta$-deformations of the ${\cal N} = 4$ super Yang-Mills theory and the
gravity duals for non-commutative gauge theories. We also discuss
non-integrable backgrounds such as AdS$_5\times T^{1,1}$ as a generalization.
