  This article presents a survey of recent developments on pseudodifferential
operators on noncommutative tori. We describe currently available constructions
of those operators: by means of a $C^*$--dynamical system, by using an analogue
of the Fourier series representation of a function in the (commutative) torus
$C^\infty(\mathbb{T}^n)$, as Rieffel deformations of the standard
pseudodifferential operators on $C^\infty(\mathbb{T}^n)$, and in association to
certain spectral triples.
