assuming the natural compactification x of a hypersurface in $(c^*)^n$ is smooth, it can exhibit any kodaira dimension depending on the size and shape of the newton polyhedron of x. in a joint work with ludmil katzarkov, we give a construction for the expected mirror symmetry partner of a complete intersection x in a toric variety which works for any kodaira dimension of x. the mirror dual might be reducible and is equipped with a sheaf of vanishing cycles. we give evidence for the duality by proving the symmetry of the hodge numbers when x is a hypersurface. the leading example will be the mirror of a genus two curve. if time permits, we will explain relations to homological mirror symmetry and the gross-siebert construction.