Multi-party conversations (MPC) are a more practical and challenging scenario involving more than two interlocutors. This research topic has drawn significant attention from both academia and industry, and it is nowadays counted as one of the most promising research areas in the field of dialogue systems. In general, MPC algorithms aim at addressing the issues of Who saying What to Whom, specifically, who speaks, say what, and address whom. The complicated interactions between interlocutors, between utterances, and between interlocutors and utterances develop many variant tasks of MPC worth investigation. In this tutorial, we present a comprehensive survey of recent advances in MPC. In particular, we summarize recent advances on the research of MPC modeling which is categorized by Who saying What to Whom. Finally, we highlight the challenges which are not yet well addressed in MPC and present future research directions.