  Phononic crystals and acoustic metamaterials are periodic structures whose
effective properties can be tailored at will to achieve extreme control on wave
propagation. Their refractive index is obtained from the homogenization of the
infinite periodic system, but it is possible to locally change the properties
of a finite crystal in such a way that it results in an effective gradient of
the refractive index (GRIN). In such case the propagation of waves can be
accurately described by means of ray theory, and different refractive devices
can be designed in the framework of wave propagation in inhomogeneous media. In
this paper we review the different devices that have been studied for the
control of both bulk or guided acoustic waves based on graded phononic
crystals.
