The rapid rise of Large Language Models (LLMs) has created new disruptive possibilities for persuasive communication, enabling fully-automated, personalized, and interactive content generation at an unprecedented scale. In this paper, we survey the emerging field of LLM-based persuasion, reviewing empirical studies that measure the influence of LLM Systems on human attitudes and behaviors. We categorize applications across domains such as politics, marketing, public health, e-commerce, and charitable giving, finding that such systems have frequently achieved human-level or even superhuman persuasiveness. Synthesizing recent evidence, we identify key factors influencing this effectiveness, including the interaction approach, model scale and capability, prompt design, personalization, and AI source disclosure. Furthermore, we critically examine the experimental designs and success metrics used to evaluate these Systems, distinguishing between direct behavioral outcomes and proxy indicators. Our survey suggests that the current capabilities of LLM-based persuasion pose profound ethical and societal risks, including to information integrity, fairness and inclusion, privacy, and individual autonomy. These risks underscore the urgent need for ethical guidelines and updated regulatory frameworks to avoid the widespread deployment of irresponsible and harmful LLM Systems.