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Many important synchronization problems in distributed computing are impossible to solve (in a fault-tolerant manner) in purely asynchronous systems, where message transmission delays and relative processor speeds are unbounded. It is then natural to seek for the minimal synchrony assumptions that are sufficient to solve a given synchronization problem. A convenient way to describe synchrony assumptions is using the failure detector abstraction. In this thesis, we determine the weakest failure detectors for several fundamental problems in distributed computing: solving fault-tolerant mutual exclusion, solving non-blocking atomic commit, and boosting the synchronization power of atomic objects. We conclude the thesis by a perspective on the very definition of failure detectors.