Multi-party conversations (MPCs) 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 says 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 MPCs worth investigation. In this paper, we present a comprehensive survey of recent advances in text-based MPCs. In particular, we first summarize recent advances on the research of MPC context modeling including dialogue discourse parsing, dialogue flow modeling and self-supervised training for MPCs. Then we review the state-of-the-art models categorized by Who says What to Whom in MPCs. Finally, we highlight the challenges which are not yet well addressed in MPCs and present future research directions.