This dissertation investigates cost-based object query optimization techniques. We focus on cost-based optimization, which has been adopted by all commercial relational database management systems (DBMSs). We identify several practical issues in developing cost-based optimizers for object queries. To attack these issues, we propose an algebraic framework for cost-based object query optimization with special attention paid to queries involving collection-valued attributes (CVAs) and multiple collection types. Our work contributes to research and engineering of cost-based object query optimization in four aspects: the algebra, the unnesting algorithm, the reference materialization technique, and the cost model.