  We explore a number of examples of special Lagrangian fibrations on
non-compact Calabi-Yau manifolds invariant under torus actions. These include
fibrations on crepant resolutions of canonical toric singularities (already
found by Goldstein), proper versions of these fibrations, and fibrations on
flat deformations of canonical toric singularities. We do this with an eye
towards understanding the global structure and discriminant loci of such
fibrations.
  The paper ends with some speculation, both about local mirror symmetry, and
the connections of this work with the work of W.D. Ruan and D. Joyce. In the
last section, we discuss the philosophy of the Strominger-Yau-Zaslow conjecture
in the light of a number of recent ideas of myself and Wilson, Kontsevich and
Soibelman, and Joyce.
