The Kahler-like condition is introduced by Yang-Zheng and Angella-Otal-Ugarte-Villacampa, which says the curvature of a metric connection has the same symmetry as the one of a Kahler metric. In this talk, we mainly discuss when the Bismut-Strominger connection is Kahler-like, BKL for short, and show several structural theorems on BKL manifolds and their relevant manifolds.