Abstract We consider the theories obtained by modding tensor products of N = 2 superconformal coset theories by discrete symmetries. A large class of (2,2) and (0,2) heterotic string compactifications is obtained by modding by products of Z N and permutation symmetries and by adding discrete torsion and/or background gauge fields. The presence of discrete torsion modifies the usual generalized GSO projection and gives rise to (2,2), (0,2) or non-supersymmetric compactifications depending on its (quantized) value. We present results from a systematic scan for new (2,2) compactifications obtained through these moddings. We also construct left-right asymmetric compactifications by twisting different left- and right-movers of the N = 2 blocks. Some of these constructions provide a generalization of the concept of asymmetric orbifolds to non-toroidal (Calabi-Yau) compactification varieties. We prove that all these models can be interpreted as left-right symmetric compactifications in the presence of discrete torsion. As an application of the above ideas we also build three-generation SU(3) × SU(2) × U(1) string models by appropriately modding the 1 9 heterotic string compactification.