In the rapidly evolving field of conversational AI, Ontology Expansion (OnExp) is crucial for enhancing the adaptability and robustness of conversational agents. Traditional models rely on static, predefined ontologies, limiting their ability to handle new and unforeseen user needs. This survey paper provides a comprehensive review of the state-of-the-art techniques in OnExp for conversational understanding. It categorizes the existing literature into three main areas: (1) New Intent Discovery, (2) New Slot-Value Discovery, and (3) Joint OnExp. By examining the methodologies, benchmarks, and challenges associated with these areas, we highlight several emerging frontiers in OnExp to improve agent performance in real-world scenarios and discuss their corresponding challenges. This survey aspires to be a foundational reference for researchers and practitioners, promoting further exploration and innovation in this crucial domain.