  This is an outline of work in progress concerning an algebro-geometric form
of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of
degeneration of Calabi-Yau manifolds, which we call toric degenerations. For
these, the degenerate fibre is a union of toric varieties meeting along toric
strata. In addition, the total space must look locally toric outside of some
singular set. This is a generalisation of both Mumford-type degenerations of
abelian varieties and degenerations of Calabi-Yau hypersurfacesin toric
varieties. From such a degeneration, we construct a dual intersection graph
along with a singular affine structure. We also explain how to reverse this
procedure, using logarithmic structures. We then use a discrete Legendre
transform on these affine manifolds to recover mirror symmetry. Finally, we
discuss the relationship between this construction and more classical forms of
SYZ.
  The details of the ideas presented here will appear elsewhere.
