Amazonis Planitia, located between the two main volcanic provinces on Mars (Tharsis and Elysium), is characterized by extremely smooth topography at several scale lengths, as smooth as oceanic abyssal plains topography on Earth. We use Mars Global Surveyor (MGS) data (primarily very high resolution Mars Orbiter Laser Altimeter (MOLA) topography and derivative slope maps, gradient maps, and detrended maps) to examine the surface morphology of Amazonis Planitia and the stratigraphic relationships among previously mapped and newly defined units. These new data reveal the presence of a 1300 km diameter Noachian impact basin in northwest Amazonis Planitia and an extensive Late Hesperian lava flow unit that appears to have originated from the Olympus Mons source area prior to aureole formation. The presence of this previously unrecognized flow unit strongly suggests that Olympus Mons activity dates back to at least the Hesperian, as did activity on the Tharsis Montes. Emplacement of this ~100 meter thick flow unit formed a barrier along the northern margin of Amazonis Planitia which had a profound influence on the subsequent geologic history of the region. Formation of Olympus Mons aureole deposits created an eastern topographic barrier, and subsequent Tharsis Montes lava flows entered the basin from the south, flowing around the aureole. These three barriers (degraded Noachian crater rim, proto-Olympus Mons flow unit, and Olympus Mons aureole) caused subsequent lava flows and outflow channel effluents, primarily from the Elysium region to the west, to pond on the floor of Amazonis Planitia, preferentially smoothing the terrain there. Mars Orbiter Camera (MOC) images substantiate that at least two very fluid lava flows alternated with fluvial episodes from Elysium Planitia, flowing through Marte Valles onto the floor of the Amazonis Planitia basin. Within Amazonis Planitia, MOC images show flow-like textures heavily mantled by sediments, and radar data reveal the presence of rough lava flow surfaces underlying the sedimentary debris. These data thus suggest that the unique smoothness of Amazonis Planitia is the result of deposition of thin fluid lava flows and fluvial sediments in an enclosed basin. Crater counts suggest that the most recent resurfacing may have occurred in the latest Amazonian Period, in the last 1% of the history of Mars. In light of its unique history, it is somewhat ironic to note that Amazonis Planitia was originally thought to be a typical young Martian surface and therefore used to name the Amazonian era.