Some aspects of limiting mixed Hodge structures

Limiting mixed Hodge structures is a classical concept in complex Kähler geometry which has been introduced by P. Griffiths, P. Deligne and W. Schmid. Deligne's conjecture, supported by recent work of Ayoub and Levine, predicts that if the limit arises from a geometric family, then the limiting object comes really from a mixed Hodge structure  of  algebraic varieties. The question is then how to recover those algebraic varieties directly from the geometry of the family.