The Podleś spheres, which are q-deformed analogues of the 2-sphere, are among the most classical objects in non-commutative geometry, but only quite  recently their structure as quantum metric spaces has begun to unravel.   In my talk, I will first provide a basic introduction to Rieffel’s theory of compact quantum metric spaces and his non-commutative counterpart to the Gromov-Hausdorff distance, and then present some recent results showing that the quantised 2-spheres actually converge (in the quantum Gromov-Hausdorff distance) to the classical round 2-sphere as the deformation parameter q tends to 1. The talk is based on joint work with Konrad Aguilar, Thomas Gotfredsen and Jens Kaad.