  We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds
considering their elliptic genera. Under the duality (or mirror) transform
performed by orbifoldizing the Landau-Ginzburg model via some discrete group of
the superpotential we observe that the roles of the untwisted and twisted
sectors are exchanged. As explicit evidence detailed orbifold data are
presented for $N=2$ minimal models, Arnold's exceptional singularities, $K3$
surfaces constructed from Arnold's singularities and Fermat hypersurfaces. (To
appear in the proceedings of the workshop, ``Quantum Field Theory, Integrable
Models and Beyond'', Yukawa Institute for Theoretical Physics, Kyoto
University, 14-18 February 1994.)
