  This contribution to the 2015 AMS Summer Institute in Algebraic Geometry
(Salt Lake City) announces a general mirror construction. This construction
applies to log Calabi-Yau pairs (X,D) with maximal boundary D or to maximally
unipotent degenerations of Calabi-Yau manifolds. The new ingredient is a notion
of "punctured Gromov-Witten invariant", currently in progress with Abramovich
and Chen. The mirror to a pair (X,D) is constructed as the spectrum of a ring
defined using the punctured invariants of (X,D). An analogous construction
leads to mirrors of Calabi-Yau manifolds. This can be viewed as a
generalization of constructions developed jointly with Hacking and Keel in the
case of log CY surfaces and K3 surfaces.
