Automated Program Repair (APR) is a crucial task in software development and maintenance, aiming to patch software bugs automatically without human intervention. The rise of Large Language Models (LLMs) has significantly advanced APR. However, as researchers delve deeper into APR as a downstream task for LLMs, a key challenge remains: how to effectively integrate APR-specific information to complement LLMs capabilities. This survey revisits 124 existing APR studies, most from 2021 to 2024, from two perspectives: Utilizing LLMs and APR-specific Information. First, we define the concept of APR-specific information. Then, we summarize techniques for utilizing LLMs in patch generation in four dimensions. Next, we explore critical factors influencing the effectiveness of generating patches by LLMs, such as prompting context and fine-tuning configurations. After that, we focus on the evaluation of generated patches, including benchmarks, reasoning cost scaling, etc. Furthermore, we distill all APR-specific information (e.g., bug-fix pairs and error messages), highlighting their unique importance and features. Finally, we comprehensively outline challenges, limitations, and potential future research directions in APR in the LLM era. To conclude, by adopting the two perspectives, we aim to provide valuable insights into mining and leveraging APR-specific information in utilizing LLMs process for the APR community.