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Compared to traditional sentiment analysis, which only considers text, multimodal sentiment analysis needs to consider emotional signals from multimodal sources simultaneously and is therefore more consistent with the way how humans process sentiment in real-world scenarios. It involves processing emotional information from various sources such as natural language, images, videos, audio, physiological signals, etc. However, although other modalities also contain diverse emotional cues, natural language usually contains richer contextual information and therefore always occupies a crucial position in multimodal sentiment analysis. The emergence of ChatGPT has opened up immense potential for applying large language models (LLMs) to text-centric multimodal tasks. However, it is still unclear how existing LLMs can adapt better to text-centric multimodal sentiment analysis tasks. This survey aims to (1) present a comprehensive review of recent research in text-centric multimodal sentiment analysis tasks, (2) examine the potential of LLMs for text-centric multimodal sentiment analysis, outlining their approaches, advantages, and limitations, (3) summarize the application scenarios of LLM-based multimodal sentiment analysis technology, and (4) explore the challenges and potential research directions for multimodal sentiment analysis in the future.