Many important materials processes take place on time scales that vastly exceed the nanoseconds accessible to molecular dynamics simulation. Typically, this long-time dynamical evolution is characterized by a succession of thermally activated infrequent events involving defects in the material. Over the last two decades, we have been developing a new class of methods, accelerated molecular dynamics, in which the known characteristics of infrequent-event systems are exploited to make reactive events take place more frequently, in a dynamically correct way. For a range of processes, this approach has been remarkably successful, offering a view of complex dynamical evolution on time scales of microseconds, milliseconds, and sometimes beyond. Examples include metallic surface diffusion and growth, processes important during radiation damage and radiation damage annealing, and dynamics of nanotubes and nanoscale clusters. Many other systems should be amenable to this type of treatment as well. After an introduction to these methods, I will present some recent results and some recent advances, including our new understanding of the generality of parallel replica dynamics and some novel ways to parallelize AMD methods.