i will first give an introduction to the notion of the curvature operator of the second kind and review some known results, including the proof of nishikawa's conjecture stating that a closed riemannian manifold with positive (resp. nonnegative) curvature operator of the second is diffeomorphic to a spherical space form (resp. a riemannian locally symmetric space). then i will talk about my recent works on the curvature operator of the second kind on kahler manifolds and product manifolds. along the way, i will mention some interesting questions and conjectures.