We present an overview of the HERschel Inventory of The Agents of Galaxy Evolution (HERITAGE) in the Magellanic Clouds project, which is a Herschel Space Observatory open time key program. We mapped the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) at 100, 160, 250, 350, and 500{mu}m with the Spectral and Photometric Imaging Receiver (SPIRE) and Photodetector Array Camera and Spectrometer (PACS) instruments on board Herschel using the SPIRE/PACS parallel mode. The overriding science goal of HERITAGE is to study the life cycle of matter as traced by dust in the LMC and SMC. The far-infrared and submillimeter emission is an effective tracer of the interstellar medium (ISM) dust, the most deeply embedded young stellar objects (YSOs), and the dust ejected by the most massive stars. We describe in detail the data processing, particularly for the PACS data, which required some custom steps because of the large angular extent of a single observational unit and overall the large amount of data to be processed as an ensemble. We report total global fluxes for the LMC and SMC and demonstrate their agreement with measurements by prior missions. The HERITAGE maps of the LMC and SMC are dominated by the ISM dust emission and bear most resemblance to the tracers of ISM gas rather than the stellar content of the galaxies. We describe the point source extraction processing and the criteria used to establish a catalog for each waveband for the HERITAGE program. The 250{mu}m band is the most sensitive and the source catalogs for this band have ~25,000 objects for the LMC and ~5500 objects for the SMC. These data enable studies of ISM dust properties, submillimeter excess dust emission, dust-to-gas ratio, Class 0 YSO candidates, dusty massive evolved stars, supernova remnants (including SN1987A), HII regions, and dust evolution in the LMC and SMC. All images and catalogs are delivered to the Herschel Science Center as part of the community support aspects of the project. These HERITAGE images and catalogs provide an excellent basis for future research and follow up with other facilities.
