Weighted composition operators on the Bloch space of a bounded homogeneous domain

In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in ${\mathbb{C}}^n$ with particular emphasis on the issues of boundedness and compactness. We also discuss the bounded and the compact weighted composition operators from the Bloch space to the Hardy space $H^{\mathrm{\infty }}$.