This paper delves into the applications of generative artificial intelligence (GAI) in semantic communication (SemCom) and presents a thorough study. Three popular SemCom systems enabled by classical GAI models are first introduced, including variational autoencoders, generative adversarial networks, and diffusion models. For each system, the fundamental concept of the GAI model, the corresponding SemCom architecture, and the associated literature review of recent efforts are elucidated. Then, a novel generative SemCom system is proposed by incorporating the cutting-edge GAI technology-large language models (LLMs). This system features two LLM-based AI agents at both the transmitter and receiver, serving as "brains" to enable powerful information understanding and content regeneration capabilities, respectively. This innovative design allows the receiver to directly generate the desired content, instead of recovering the bit stream, based on the coded semantic information conveyed by the transmitter. Therefore, it shifts the communication mindset from "information recovery" to "information regeneration" and thus ushers in a new era of generative SemCom. A case study on point-to-point video retrieval is presented to demonstrate the superiority of the proposed generative SemCom system, showcasing a 99.98% reduction in communication overhead and a 53% improvement in retrieval accuracy compared to the traditional communication system. Furthermore, four typical application scenarios for generative SemCom are delineated, followed by a discussion of three open issues warranting future investigation. In a nutshell, this paper provides a holistic set of guidelines for applying GAI in SemCom, paving the way for the efficient implementation of generative SemCom in future wireless networks.