Traditional techniques for synchronization are based on \emph{locking} that provides threads with exclusive access to shared data. \emph{Coarse-grained} locking typically forces threads to access large amounts of data sequentially and, thus, does not fully exploit hardware concurrency. Program-specific \emph{fine-grained} locking or \emph{non-blocking} (\emph{i.e.}, not using locks) synchronization, on the other hand, is a dark art to most programmers and trusted to the wisdom of a few computing experts. Thus, it is appealing to seek a middle ground between these two extremes: a synchronization mechanism that relieves the programmer of the overhead of reasoning about data conflicts that may arise from concurrent operations without severely limiting the program's performance. The \emph{Transactional Memory (TM)} abstraction is proposed as such a mechanism: it intends to combine an easy-to-use programming interface with an efficient utilization of the concurrent-computing abilities provided by multicore architectures. TM allows the programmer to \emph{speculatively} execute sequences of shared-memory operations as \emph{atomic transactions} with \emph{all-or-nothing} semantics: the transaction can either \emph{commit}, in which case it appears as executed sequentially, or \emph{abort}, in which case its update operations do not take effect. Thus, the programmer can design software having only sequential semantics in mind and let TM take care, at run-time, of resolving the conflicts in concurrent executions. Intuitively, we want TMs to allow for as much \emph{concurrency} as possible: in the absence of severe data conflicts, transactions should be able to progress in parallel. But what are the inherent costs associated with providing high degrees of concurrency in TMs? This is the central question of the thesis.