Parallel replica dynamics was proposed by A.F. Voter as a tool for
accelerating molecular dynamics simulations characterized by a sequence of
infrequent, but rapid, transitions from one state to another. An example would
be the migration of a defect through a crystal. Parallel replica dynamics
accelerates this by simulating many replicas simultaneously, concatenating the
simulation times of the realizations as though it were a single long
trajectory. This motivates important questions: Is parallel replica dynamics
algorithm doing what we hope? For what systems will it be useful? How do we
implement it efficiently? In this talk, I will thoroughly describe the
algorithm and report on progress towards rigorous justification. Open
questions and related problems will also be discussed.