views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: binary search trees, adaptive algorithms, splay trees, Unified Bound, dynamic A ubiquitous problem in the field of algorithms and data structures is that of searching for an element from an ordered universe. The simple yet powerful binary search tree (BST) model provides a rich family of solutions to this problem. Although BSTs require Ω(lg n) time per operation in the worst case, various adaptive BST algorithms are capable of exploiting patterns in the sequence of queries to achieve tighter, input-sensitive, bounds that can be o(lg n) in many cases. This thesis furthers our understanding of what is achievable in the BST model along two directions. First, we make progress in improving instance-specific lower bounds in the BST model. In particular, we introduce a framework for generating lower bounds on the cost that any BST algorithm must pay to execute a query sequence,