One can give precise meaning to statements in the literature of high-energy physics of the kind "Matrix algebras converge to the sphere". This can be done by introducing and applying the concept of a "compact quantum metric space", and a corresponding "quantum Gromov-Hausdorff distance". But the physics literature continues with discussion of superstructure in this situation, such as vector bundles, connections, Dirac operators, etc. For example, certain projective modules over matrix algebras are asserted to be the monopole bundles corresponding to the usual monopole bundles on the sphere. This suggests that one needs to make precise the idea that for two compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles over the other space. In a recent paper M. A. Rieffel showed how to do this for ordinary metric spaces. The aim of this meeting is to study strategy and analyse most recent progress in extending these results to the case of quantum metric spaces.