Mining social web text has been at the heart of the Natural Language Processing and Data Mining research community in the last 15 years. Though most of the reported work is on widely spoken languages, such as English, the significance of approaches that deal with less commonly spoken languages, such as Greek, is evident for reasons of preserving and documenting minority languages, cultural and ethnic diversity, and identifying intercultural similarities and differences. The present work aims at identifying, documenting and comparing social text data sets, as well as mining techniques and applications on social web text that target Modern Greek, focusing on the arising challenges and the potential for future research in the specific less widely spoken language.