On a Kaehler manifold, one can define the holomorphic sectional curvature as the Riemannian sectional curvature restricted on any $J$-invariant real $2$-plane. Compact Kaehler manifolds with positive holomorphic sectional curvature form an interesting class of Kaehler manifolds. I will talk about some recent characterization of such manifolds, and propose a question to study the space of all Kaehler metrics of positive holomorphic sectional curvature on a given Kaehler manifold.