String dualities allow us the non-geometric string backgrounds whose transition functions involve duality transformations. We first discuss such non-geometric backgrounds obtained through T-duality, i.e. T-folds, from the world-sheet point of view. In particular, we construct their modular invariant partition functions systematically based on the momentum lattices. Second, as an application, we show that our non-geometrical setting, or its analogs, can simply realize non-supersymmetric backgrounds with vanishing cosmological constant at one loop, as well as non-supersymmetric D-branes with vanishing self-overlap, which give non-perturbatively small cosmological constant. If time is allowed, we would also like to comment on the world-sheet theories obtained from conformal interfaces.