How does indexing interact with SQL query optimization, and how can you influence the query optimizer to use your indexes?

The query optimizer analyzes queries and chooses the most efficient execution plan, often utilizing indexes. You can influence the optimizer by ensuring your queries are well-written (avoiding functions in `WHERE` clauses, using appropriate data types), keeping statistics up-to-date (so the optimizer has accurate information about data distribution), and using hints (though hints should be used cautiously as they can prevent the optimizer from adapting to changes). Analyzing execution plans is key to understanding how the optimizer is using (or not using) your indexes.