By providing fully spatio-temporally-resolved atomistic trajectories, Molecular Dynamics (MD) simulations can reveal fundamental characteristics of the thermodynamics and kinetics of materials. While the exponential increase in computing power and the advance of modern data-science techniques since the method was introduced in the late 1950s has dramatically extended the spatial reach of MD, as well as allowed a significant increase in the fidelity of simulations, the accessible simulation timescales have remained limited by the fundamentally sequential nature of the numerical solution of atomic equations of motion, often confining simulations to sub-microsecond timescales even on modern computers. This stringent restriction strongly limits the ability of MD to directly observe the rare, thermally-activated, reactions that underpin vast swaths of chemistry, biology, and materials science. In this contribution, we present a family of methods based on MD – the so-called Accelerated MD (AMD) methods – that were developed to alleviate this limitation. Each AMD method will be introduced, its mathematical justification presented, its recent generalizations discussed, and illustrative applications presented.