We present recent progress on the solution of WZW models based on type I supergroups. The spectrum is derived in the minisuperspace limit and extrapolated to the full WZW model. The main feature is the occurence of indecomposable non-chiral representations which are responsible for the logarithmic behaviour of correlation functions. The talk will consist of three parts: 1. Representation theory of Lie superalgebras, 2. general type I supergroup WZW models and 3. particularities of the PSU(1,1/2) WZW model. If the audience has enough stamina we can also discuss certain aspects of special marginal deformations of the PSU(1,1/2) WZW model which describe AdS(3)xS(3) with mixed RR and NS fluxes.