In the evolving landscape of online communication, moderating hate speech (HS) presents an intricate challenge, compounded by the multimodal nature of digital content. This comprehensive survey delves into the recent strides in HS moderation, spotlighting the burgeoning role of large language models (LLMs) and large multimodal models (LMMs). Our exploration begins with a thorough analysis of current literature, revealing the nuanced interplay between textual, visual, and auditory elements in propagating HS. We uncover a notable trend towards integrating these modalities, primarily due to the complexity and subtlety with which HS is disseminated. A significant emphasis is placed on the advances facilitated by LLMs and LMMs, which have begun to redefine the boundaries of detection and moderation capabilities. We identify existing gaps in research, particularly in the context of underrepresented languages and cultures, and the need for solutions to handle low-resource settings. The survey concludes with a forward-looking perspective, outlining potential avenues for future research, including the exploration of novel AI methodologies, the ethical governance of AI in moderation, and the development of more nuanced, context-aware systems. This comprehensive overview aims to catalyze further research and foster a collaborative effort towards more sophisticated, responsible, and human-centric approaches to HS moderation in the digital era.\footnote{ \textcolor{red}{WARNING: This paper contains offensive examples.

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