Symbolic regression (SR) is an optimization problem that identifies the most suitable mathematical expression or model to fit the observed dataset. Over the past decade, SR has experienced rapid development due to its interpretability and broad applicability, leading to numerous algorithms for addressing SR problems and a steady increase in practical applications. Given the lack of a comprehensive review of the current literature on SR and its significance to both academia and industry, this article provides an in-depth overview of SR. The survey begins by outlining the background of SR and introducing it from three aspects: its definition, benchmarking datasets, and evaluation metrics. We also highlight the latest advancements in SR, summarizing the current research status. The review focuses on deterministic methods, genetic programming methods, and neural network methods, offering a thorough analysis of the advantages and limitations of various algorithms. Following this, key application scenarios of SR are introduced, and some commonly used software tools are summarized. Finally, the article provides an outlook on future research directions. This survey reviews the latest developments in SR and offers insightful guidance for readers who are new to the field.