To optimize the performance of a SQL database handling large volumes of data, start by indexing the most frequently queried columns to speed up search and retrieval. Ensure that your queries are optimized, avoiding unnecessary complexity and using JOINs and subqueries efficiently. Partition large tables to distribute the load and improve query performance. Regularly update statistics and maintain your indexes to prevent fragmentation. Also, consider using database caching mechanisms and monitoring performance metrics to identify and address bottlenecks. Lastly, carefully plan your database schema to ensure normalization and efficient data storage.