  We survey the authors recent works, joint with A. Jacob, on
Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del
Pezzo surfaces. We discuss some applications, including the Torelli theorem for
$ALH^*$ gravitational instantons and explain how our results can be used to
prove that all $ALH^*$ gravitational instantons can be compactified to a weak
del Pezzo surface, recovering a recent result of Hein-Sun-Viaclovsky-Zhang.
