Mirror symmetry has developed into an important link between physics and mathematics and predicts that Calabi-Yau varieties come as pairs of mirrors.
In this talk I will describe an explicit mirror construction for monomial degenerations of Calabi-Yau varieties.

Using tropical geometry and Groebner basis techniques the construction is formulated in a Cox homogeneous toric setup and generalizes those for hypersurfaces and complete intersections by Batyrev and Borisov. I will also comment on the relations of the tropical construction to deformation theory.