There has been extensive work in query optimization since the early ’70’s. It is hard to capture the breadth and depth of this large body of work in a short article. Therefore, I have decided to focus primarily on the optimization of SQL queries in relational database systems and present my biased and incomplete view of this field. The goal of this article is not to be comprehensive, but rather to explain the foundations and present samplings of significant work in this area. I would like to apologize to the many contributors in this area whose work I have failed to explicitly acknowledge due to oversight or lack of space. I take the liberty of trading technical precision of ease of presentation.