In this talk we will discuss the geometry of Strominger connection of Hermitian manifolds, based on recent joint works with Quanting Zhao. We will focus on two special types of Hermitian manifolds: Strominger Kaehler-like (SKL) manifolds, and Strominger parallel torsion (SPT) manifolds. The first class means Hermitian manifolds whose Strominger connection (also known as Bismut connection) has curvature tensor obeying all Kaehler symmetries, and the second class means Hermitian manifolds whose Strominger conneciton has parallel torsion. We showed that any SKL manifold is SPT, which is known as (an equivalent form of) the AOUV Conjecture (namely, SKL implies pluriclosedness). We obtained a characterization theorem for SPT condition in terms of Strominger curvature, which generalizes the previous theorem. We will also discuss examples and some structural results for SKL and SPT manifolds.