A plasma consists of a fluid of positive and negative charged particles, generally created by heating or photo-ionizing (direct / tunneling / multi-photon / barrier-suppression) a dilute gas. Under normal conditions the plasma will be macroscopically neutral (or quasi-neutral), an equal mix of electrons and ions in equilibrium. However, if a strong enough external electric or electromagnetic field is applied, the plasma electrons, which are very light in comparison to the background ions (by a factor of 1836), will separate spatially from the massive ions creating a charge imbalance in the perturbed region. A particle injected into such a plasma would be accelerated by the charge separation field, but since the magnitude of this separation is generally similar to that of the external field, apparently nothing is gained in comparison to a conventional system that simply applies the field directly to the particle. But, the plasma medium acts as the most efficient transformer (currently known) of the transverse field of an electromagnetic wave into longitudinal fields of a plasma wave. In existing accelerator technology various appropriately designed materials are used to convert from transverse propagating extremely intense fields into longitudinal fields that the particles can get a kick from. This process is achieved using two approaches: standing-wave structures (such as resonant cavities) or traveling-wave structures such as disc-loaded waveguides etc. But, the limitation of materials interacting with higher and higher fields is that they eventually get destroyed through ionization and breakdown. Here the plasma accelerator science provides the breakthrough to generate, sustain, and exploit the highest fields ever produced by science in the laboratory.