The solution of 2D Sigma models on superspaces (-groups,-cosets, etc.) is a problem with various potential applications in condensed matter theory and string theory, in particular in the context of the AdS/CFT correspondence. At the example of the PSU(1,1/ 2) sigma model, I shall illustrate some of the intriguing novel features of such theories, review a few recent results and assess the prospects for a complete or partial solution.