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In this paper, we establish a structure theorem for projective klt pairs$(X,\Delta)$ with nef anti-log canonical divisor; specifically, we prove that,up to replacing $X$ with a finite quasi-\'etale cover, $X$ admits a locallytrivial rationally connected fibration onto a projective klt variety withnumerically trivial canonical divisor. This structure theorem generalizesprevious works for smooth projective varieties and reduces several structureproblems to the singular Beauville-Bogomolov decomposition for Calabi-Yauvarieties. As an application, projective varieties of klt Calabi-Yau type,which naturally appear as an outcome of the Log Minimal Model Program, aredecomposed into building block varieties: rationally connected varieties andCalabi-Yau varieties.

Structure theorem for projective klt pairs with nef anti-canonical divisor