Over the past few years, it has been shown that, when integrating out the spacetime dependence with a certain integration measure, some four-point correlation functions in N=4 super Yang-Mills (SYM) can be computed exactly. These physical observables are often called integrated correlators, which are functions of Yang-Mills coupling \tau, and transform under S-duality of N=4 SYM. In this talk, I will review some of the recent developments regarding these integrated correlators. In particular, I will discuss the so-called Laplace-difference equations that determine the integrated correlators recursively. I will also present the generating functions of the integrated correlators that resum the ranks of the gauge group and the charges of the operators, from which we will further determine the large-N and large-charge properties of the integrated correctors.