  We introduce the notion of Wall-Crossing Structure and discuss it in several
examples including complex integrable systems, Donaldson-Thomas invariants and
Mirror Symmetry.
  For a big class of non-compact Calabi-Yau 3-folds we construct complex
integrable systems of Hitchin type with the base given by the moduli space of
deformations of those 3-folds. Then Donaldson-Thomas invariants of the Fukaya
category of such a Calabi-Yau 3-fold can be (conjecturally) described in two
more ways: in terms of the attractor flow on the base of the corresponding
complex integrable system and in terms of the skeleton of the mirror dual to
the total space of the integrable system.
  The paper also contains a discussion of some material related to the main
subject, e.g. Betti model of Hitchin systems with irregular singularities, WKB
asymptotics of connections depending on a small parameter, attractor points in
the moduli space of complex structures of a compact Calabi-Yau 3-fold, relation
to cluster varieties, etc.
