  We review the coset construction of conformal field theories; the emphasis is
on the construction of the Hilbert spaces for these models, especially if fixed
points occur. This is applied to the $N=2$ superconformal cosets constructed by
Kazama and Suzuki. To calculate heterotic string spectra we reformulate the
Gepner con- struction in terms of simple currents and introduce the so-called
extended Poincar\'e polynomial. We finally comment on the various equivalences
arising between models of this class, which can be expressed as level rank
dualities. (Invited talk given at the III. International Conference on
Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June
1993. To appear in Theor. Math. Phys.)
