Here are two results that Marc Rieffel has proved about non-commutative tori: 1. A pair of two dimensional non-commutative tori are Morita equivalent if and only if their deformation parameters lie in the same orbit of a particular action of GL2(Z). (Here Pimsner and Voiculescu helped.) 2. To each Poisson structure on a torus there is a canonical construction of a Moyal deformation of the algebra of functions on the torus, as well as a corresponding non-commutative torus. (The two algebras are isomorphic, and in this instance provide a bridge between the worlds of non-commutative geometry and deformation theory.) In this talk I will define all of the relevant terminology and go over these two results. Then, using the second result, I will arrive at the following interesting interpretation of the first: the Morita equivalences between quantum tori are generated by two types of transformations- one of which can be interpreted as an interchange between the meridians and latitudes of the torus, and the other as a non-commutative T-duality.