In 1831, Faraday reported to the Royal Society of London that granular material inside a container, when vibrated, would spontaneously begin to exhibit convection rolls, similar to what is observed in normal fluids when heated from below. This observation indicated that not only can a granular material act like a fluid, but also that vibrations can affect the properties of these materials in important ways. Such phenomena are of immediate practical importance because granular materials exist all around us. We use sand and gravel to build the roads we drive on; we process grain to provide our food supply; we mine ore to provide coal, minerals, and precious commodities; we take powders and pills to cure what ails us. Many of the phenomena observed in granular media are prototypical examples of complex, nonequilibrium behavior that is also found in an increasing number of other systems. As a result, sandpiles have served as a macroscopic and visually appealing metaphor for thinking about a number of microscopic systems that are not directly accessible to our senses. Despite the common occurrence of these materials, their properties are not at all well understood and most of our knowledge centers on the subset of static, equilibrium properties of granular matter. Only over the last few years have physicists and engineers begun to unravel some of the exceptional time-dependent, nonequilibrium properties that these seemingly simple materials exhibit. This review focuses on recent developments in the newly emerging field of granular dynamics and, in particular, addresses the role of vibration in determining the phenomena observed in such media.