  Advanced algorithms are necessary to obtain faster-than-real-time dynamic
simulations in a number of different physical problems that are characterized
by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms
that preserve the dynamics of the model are described. These include the
$n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC)
algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use
of these algorithms, they are applied to some simplified models of dynamic
physical systems. The models studied include a model for ion motion through a
pore such as a biological ion channel and the metastable decay of the
ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic
algorithms, which are in the class of parallel discrete event simulations, are
discussed. Efforts are made to keep the article at an elementary level by
concentrating on a simple model in each case that illustrates the use of the
advanced dynamic Monte Carlo algorithm.
