Responsible Generative AI: What to Generate and What Not

In recent years, generative AI (GenAI), like LLMs and text-to-image models, has received significant attention across various domains. However, ensuring the responsible generation of content by these models is crucial for their real-world applicability. This raises an interesting question: \textit{What should responsible GenAI generate, and what should it not?} To answer the question, this paper investigates the practical responsible requirements of both textual and visual generative models, outlining five key considerations: generating truthful content, avoiding toxic content, refusing harmful instruction, leaking no training data-related content, and ensuring generated content identifiable. Specifically, we review recent advancements and challenges in addressing these requirements. Besides, we discuss and emphasize the importance of responsible GenAI across healthcare, education, finance, and artificial general intelligence domains. Through a unified perspective on both textual and visual generative models, this paper aims to provide insights into practical safety-related issues and further benefit the community in building responsible GenAI.