The rapid advancement of Large AI Models (LAIMs), particularly diffusion models and large language models, has marked a new era where AI-generated multimedia is increasingly integrated into various aspects of daily life. Although beneficial in numerous fields, this content presents significant risks, including potential misuse, societal disruptions, and ethical concerns. Consequently, detecting multimedia generated by LAIMs has become crucial, with a marked rise in related research. Despite this, there remains a notable gap in systematic surveys that focus specifically on detecting LAIM-generated multimedia. Addressing this, we provide the first survey to comprehensively cover existing research on detecting multimedia (such as text, images, videos, audio, and multimodal content) created by LAIMs. Specifically, we introduce a novel taxonomy for detection methods, categorized by media modality, and aligned with two perspectives: pure detection (aiming to enhance detection performance) and beyond detection (adding attributes like generalizability, robustness, and interpretability to detectors). Additionally, we have presented a brief overview of generation mechanisms, public datasets, and online detection tools to provide a valuable resource for researchers and practitioners in this field. Furthermore, we identify current challenges in detection and propose directions for future research that address unexplored, ongoing, and emerging issues in detecting multimedia generated by LAIMs. Our aim for this survey is to fill an academic gap and contribute to global AI security efforts, helping to ensure the integrity of information in the digital realm. The project link is https://github.com/Purdue-M2/Detect-LAIM-generated-Multimedia-Survey.