Abstract: Pluriclosed metrics are a special class of Hermitian metrics that play an important role in the geometry of non-Kähler manifolds. They are characterized by the torsion of the associated Bismut connection being closed. In this talk, we present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. This is joint work with G. Barbaro and N. Tardini.