Abstract: The aim of this paper is to introduce the progress on the research for limit cycles of Li\'enard systems and present some new results. The results focus on four problems: the existence of limit cycles, the uniqueness of limit cycles, the exact number of limit cycles and the upper bound of limit cycles. Finally, we summarize some methods for studying limit cycles of Li\'enard systems.

Key words: Limit cycle; , Li\'enard system; , Existence and uniqueness of limit cycles; , Exact number oflimit cycles