The Frontier Fields are a directors discretionary time campaign with HST and the Spitzer Space Telescope to see deeper into the universe than ever before. The Frontier Fields combine the power of HST and Spitzer with the natural gravitational telescopes of massive high-magnification clusters of galaxies to produce the deepest observations of clusters and their lensed galaxies ever obtained. Six clusters - Abell 2744, MACSJ0416.1-2403, MACSJ0717.5+3745, MACSJ1149.5+2223, Abell S1063, and Abell 370 - were selected based on their lensing strength, sky darkness, Galactic extinction, parallel field suitability, accessibility to ground-based facilities, HST, Spitzer and JWST observability, and pre-existing ancillary data. These clusters have been targeted by the HST ACS/WFC and WFC3/IR with coordinated parallels of adjacent blank fields for over 840 HST orbits. The Spitzer Space Telescope has dedicated > 1000 hours of directors discretionary time to obtain IRAC 3.6 and 4.5 micron imaging to ~26.5, 26.0 ABmag 5-sigma point-source depths in the six cluster and six parallel Frontier Fields. The Frontier Field parallel fields are the second-deepest observations thus far by HST with ~29th ABmag 5-sigma point source depths in seven optical - near-infrared bandpasses. Galaxies behind the Frontier Field cluster lenses experience typical magnification factors of a few, with small regions near the critical curves magnified by factors 10-100. Therefore, the Frontier Field cluster HST images achieve intrinsic depths of ~30-33 magnitudes over very small volumes. Early studies of the Frontier Fields have probed galaxies fainter than any seen before during the epoch of reionization 6 < z < 10, mapped out the cluster dark matter to unprecedented resolution, and followed lensed transient events.