Persuasion is a fundamental aspect of communication, influencing decision-making across diverse contexts, from everyday conversations to high-stakes scenarios such as politics, marketing, and law. The rise of conversational AI systems has significantly expanded the scope of persuasion, introducing both opportunities and risks. AI-driven persuasion can be leveraged for beneficial applications, but also poses threats through unethical influence. Moreover, AI systems are not only persuaders, but also susceptible to persuasion, making them vulnerable to adversarial attacks and bias reinforcement. Despite rapid advancements in AI-generated persuasive content, our understanding of what makes persuasion effective remains limited due to its inherently subjective and context-dependent nature. In this survey, we provide a comprehensive overview of persuasion, structured around three key perspectives: (1) AI as a Persuader, which explores AI-generated persuasive content and its applications; (2) AI as a Persuadee, which examines AI's susceptibility to influence and manipulation; and (3) AI as a Persuasion Judge, which analyzes AI's role in evaluating persuasive strategies, detecting manipulation, and ensuring ethical persuasion. We introduce a taxonomy for persuasion research and discuss key challenges for future research to enhance the safety, fairness, and effectiveness of AI-powered persuasion while addressing the risks posed by increasingly capable language models.