  The present paper is dedicated to illustrating an extension of polar duality
between Fano toric varieties to a more general duality, called \emph{framed}
duality, so giving rise to a powerful and unified method of producing mirror
partners of hypersurfaces and complete intersections in toric varieties, of any
Kodaira dimension. In particular, the class of projective hypersurfaces and
their mirror partners are studied in detail. Moreover, many connections with
known Landau-Ginzburg mirror models, Homological Mirror Symmetry and Intrinsic
Mirror Symmetry, are discussed.
