Abstract New classes of unitary conformal and superconformal theories based on cosets of affine non-compact current algebras are suggested. Unitarity restrictions and the structure of the modules labelled by the primary states are discussed in general terms as well as in detail for SU (1,1)/ U (1), SU (N,M)/ SU (N) × SU (M) × U (1) and SL (2, C )/ SU (2) . Large classes of new N = 2 superconformal theories are classified and their central charges computed. This gives the non-compact counterpart of the Kazama-Suzuki models. It is shown that compact group and non-compact group Kazama-Suzuki models can be rewritten as coset models of the form (G × H)/H, where H is a maximal compact subgroup of G and G/H is kahlerian. This reveals new symmetry structures which are useful in computations. It is shown that, in applications to heterotic superstring model building in four dimensions, a c ⩽ 9 compact space can be constructed only from two non-compact N = 2 super-affine cosets based on SU (1,1) − k with k ⩾ 3 and SU (2,1) − k with k ⩾ 9 . After performing a GSO projection and heterotic conversion a la Gepner, the massless spectrum of the c = 9 SU(1,1)−3 case is analysed in detail. With some simplifying assumptions on modular invariants it is outlined how the number of families would be computed.