The adoption of the Large Language Model (LLM) has accelerated dramatically since the ChatGPT from OpenAI went online in November 2022. Recent advances in Large Multimodal Models (LMMs), which process diverse data types and enable interaction through various channels, have expanded beyond the text-to-text limitations of early LLMs, attracting significant and concurrent attention from both researchers and industry. While LLMs and LMMs are starting to spread widely, concerns about their privacy risks are increasing as well. Membership Inference Attacks (MIAs), techniques used to determine whether a particular data point was part of a model's training set, serve as a key metric for assessing the privacy vulnerabilities of machine learning models. Hu et al. show that various machine learning algorithms are vulnerable to MIA. Despite extensive studies on MIAs in traditional models, there remains a lack of systematic surveys addressing their effectiveness and implications in modern large-scale models like LLMs and LMMs. In this paper, we systematically reviewed recent studies of MIA against LLMs and LMMs. We analyzed and categorized each attack based on their methodology and scenario and discussed the limitations in existing research. Additionally, we examine privacy concerns associated with the fine-tuning process. Finally, we provided some suggestions for future research in this direction.