This paper provides a comprehensive overview of autoformalization, the process of converting informal mathematical propositions into verifiable formal representations. Driven by advances in artificial intelligence, and particularly large-scale language models (LLMs), the field of autoformalization has experienced rapid growth, bringing both new opportunities and unique challenges. In this paper, we review recent advances in autoformalization from both mathematical and LLM-centric perspectives, investigate applications of autoformalization across a range of mathematical domains and difficulty levels, and analyze the entire process from data preprocessing to model design and evaluation. We also explore the emerging role of autoformalization in increasing the verifiability of LLM-generated outputs, and highlight its potential for improving the reliability and inference capabilities of LLMs. Finally, we summarize the key open-source models and datasets that support current research, and discuss outstanding challenges and promising future directions in this field.