Query optimization is a critical component in database systems, where execution costs are minimized by identifying the most efficient query execution plan. Traditional query optimizers typically rely on fixed rules or simple heuristic algorithms to refine or select candidate plans. However, with the growing complexity of relational schemas and queries in real-world applications, such optimizers struggle to meet the demands of modern applications. Learned query optimization algorithms integrate machine learning techniques into the optimization process. They capture features of query plans and complex schemas to assist traditional optimizers. These algorithms offer innovative and effective solutions in areas such as cost modeling, join optimization, plan generation, and query rewriting. This study reviews recent achievements and developments in four main categories of learned query optimization algorithms. Future research directions are also discussed, aiming to provide a comprehensive understanding of the current state of research and to support further investigation in this field.