Dialogue systems have evolved remarkably, from rule-based dyadic interfaces to large language model (LLM) powered conversational agents. Yet the predominant focus on two-party exchanges leaves a significant gap: most real-world communication, from business meetings to online group chats, is inherently multi-party. Multi-Party Dialogue (MPD) introduces new challenges in participant tracking, discourse structure modeling, and pragmatic reasoning that simpler dyadic systems are not equipped to handle. In this survey, we present a comprehensive examination of MPD research, organized along four axes: tasks, methods, datasets, and evaluation. We trace the methodological trajectory from early statistical and supervised models, through neural and graph-based approaches, to modern LLM-driven systems and emerging multi-agent paradigms. We further synthesize benchmark resources and evaluation protocols, and identify four central bottlenecks that constrain progress: combinatorial complexity of N-party dynamics, the structural-semantic divide, evaluation inadequacy, and data scarcity. We map these challenges to concrete research opportunities, offering a roadmap for building socially intelligent, holistically evaluated MPD systems.