  In recent years, generative AI (GenAI), like large language models 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.
