The first part of this paper discusses the motivation for the Lu Qi-Keng conjecture and the results about the presence or the absence of zeroes of the Bergman kernel function of a bounded domain in C n . Its second part summarizes the main results on the Hua domains, such as the explicit Bergman kernel function, the comparison theorem for the invariant metrics, the explicit complete Einstein-Kähler metrics, the equivalence between the Einstein-Kähler metric and the Bergman metric, etc.