  Using tropical geometry we propose a mirror construction for monomial
degenerations of Calabi-Yau varieties in toric Fano varieties. The construction
reproduces the mirror constructions by Batyrev for Calabi-Yau hypersurfaces and
by Batyrev and Borisov for Calabi-Yau complete intersections. We apply the
construction to Pfaffian examples and recover the mirror given by Rodland for
the degree 14 Calabi-Yau threefold in PP^6 defined by the Pfaffians of a
general linear 7x7 skew-symmetric matrix.
  We provide the necessary background knowledge entering into the tropical
mirror construction such as toric geometry, Groebner bases, tropical geometry,
Hilbert schemes and deformations. The tropical approach yields an algorithm
which we illustrate in a series of explicit examples.
