The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classical Teichmuller theory may be viewed as a starting point of the subject, and following the work of Labourie and Goldman, many exciting developments have taken place when the target group is SL(n, R). Recent work of Kapovich, Leeb and Porti have connected the subject with geometric group theory and higher rank symmetric spaces, opening up new horizons. The aim of this discussion meeting is to expose all these recent developments on the subject and to understand avenues for further directions. The program is an immediate follow up to the ICTS Advanced School: Geometry, Groups and Dynamics-2017.