N=(2,2) supersymmetric models are of interest for mathematicians and physicists and have been used extensively as a tool for the investigation of Kaehler geometry. It is convenient to formulate and manipulate these in superspace which captures their main properties such as their full bihermitian structure. This also led to recent developments in differential geometry where these targets are characterized using structures that interpolate between complex and symplectic geometry and are defined on the sum T+T. .The research work that will be presented here extends the set of known superspace tools for the manipulation of bihermitian / generalized Kaehler geometries, namely, the gauging of isometries along directions that mix chiral and twistedchiral or semichiral multiplets. Other results that will be presented relate to possible N=(4,4) supersymmetry in semichiral models and sigma models formulation on the sum T+T. .