  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 locally
trivial rationally connected fibration onto a projective klt variety with
numerically trivial canonical divisor. This structure theorem generalizes
previous works for smooth projective varieties and reduces several structure
problems to the singular Beauville-Bogomolov decomposition for Calabi-Yau
varieties. As an application, projective varieties of klt Calabi-Yau type,
which naturally appear as an outcome of the Log Minimal Model Program, are
decomposed into building block varieties: rationally connected varieties and
Calabi-Yau varieties.
