The paper surveys the state of the art of task scheduling in Desktop Grid computing systems. We describe the general architecture of a Desktop Grid system and the computing model adopted by the BOINC middleware. We summarize research papers to bring together and examine the optimization criteria and methods proposed by researchers so far for improving Desktop Grid task scheduling (assigning tasks to computing nodes by a server). In addition, we review related papers, which address non-regular architectures, like hierarchical and peer-to-peer Desktop Grids, as well as Desktop Grids designed for solving interdependent tasks.