Euclidean Supersymmetry, Twisting and Topological Sigma Models

We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.