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Abstract 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^* C ∗ -dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus C^ ({T}ⁿ) C ∞ (T n), as Rieffel deformations of the standard pseudodifferential operators on C^ ({T}ⁿ) C ∞ (T n), and in association to certain spectral triples.
Carolina Neira Jiménez (Tue,) studied this question.