Borosilicate based glass formulations have been found suitable for vitrification of high level nuclear waste (HLW) generated during the reprocessing of spent nuclear fuel from nuclear reactors. These glasses possess desirable properties like high chemical, mechanical, thermal and radiation stability for HLW storage. Also, the amorphous nature of the glass helps accommodate the waste containing a variety of elements easily. Because of the presence of the radioactive components, such as, fission /activation products and minor actinides present in the waste, the glass containment experiences radiation damage that can significantly alter the glass structure which may influence their long term leaching behavior. Spectroscopic techniques provide direct and non-invasive method for investigating this radiation damage in the glasses. The present paper gives a glimpse of the current status and issues regarding the investigation of radiation damage in the glass matrices.