In this talk, we shall give a survey on certain developments in the field of quantum vertex algebras. More specifically, we shall begin with the definitions of a vertex algebra and a module for a vertex algebra, and then present the theory of (weak) quantum vertex algebras and modules, including a conceptual construction. Then we shall discuss $\hbar$-adic quantum vertex algebras. If time permits, we shall give an introduction to the theory of $\phi$-coordinated modules for (weak) quantum vertex algebras.