Holomorphic vector bundle, as a generalization of holomoprhic functions, is one of the central object of study in several complex variables and complex geometry. Generally speaking, we study three types of properties of holomorphic vector bundles, namely, differential geometric properties, analytic properties, and algebraic geometric properties, and their deep relations. In this lecture, we will discuss some new developments on this area and propose some open problems. This lecture is based on a series of works joint with Professor Ning, Wang, Zhang, Zhou.