The 2015 New Horizons flyby has produced the first high-resolution maps of morphology and topography of Pluto and Charon, the most distant objects so mapped. Global integrated mosaics of Pluto were produced using both LORRI framing camera and MVIC line scan camera data, showing the best resolution data obtained for all areas of the illuminated surface, ∼78% of the body. A unique feature of the Pluto imaging data set is the observation of terrains illuminated only by light scattered from atmospheric haze, allowing us to map terrains in the southern hemisphere that would otherwise have been in darkness. MVIC 4-color data were combined with the panchromatic map to produce full color global maps. Digital elevation models (DEMs) over ∼42% of Pluto were produced using combinations of MVIC hemispheric scans and LORRI mosaics, from which slopes at scales of ∼1 km can be determined. Pluto can be divided into regions each with distinct topographic signatures, corresponding with major physiographic terrain types. Large areas of Pluto are comprised of low-relief moderately cratered plains units. Deeply pitted and glaciated plains east of Sputnik Planitia are elevated ∼0.7 km. The most dominant topographic feature on Pluto is the 1200-by-2000-km wide depression enclosing the bright Sputnik Planitia ice sheet, the surface of which is 2.5-to-3.5 km deep (relative to the rim) and ∼2 km deep relative to the mean radius. The partial ring of steep-sided massifs, several of which are more than 5 km high, along the western margins of Sputnik Planitia produce some of the locally highest and steepest relief on Pluto, with slopes of 40-50°. The second major topographic feature is a complex, eroded, ridge-trough system ∼300-400 km wide and at least 3200 km long extending north-to-south along the 155° meridian. This enormous structure has several kilometers of relief. It may predate the large impact event forming the basin, though some post-Sputnik Planitia deformation is evident. The large depressed, partially walled plain, Hyecho Palus, lies due southwest of Sputnik Planitia. Near the center of Hyecho Palus lie the circular constructional edifices Wright and Piccard Montes. Wright Mons rises 4.5 km above these plains, with a central depression ∼4.5 km deep, whereas Piccard Mons, best observed in haze-light, rises ∼5.5 km above the plains but has a bowl-shaped central depression ∼5.5 km below the plains for a total relief of up to 11 km, the greatest observed on Pluto. Both of these features are interpreted as constructional (volcanic?) in nature. Additional prominent topographic features include a 2-3 km high and ∼600 km wide dome centered on the illuminated IAU pole and the amoeboidal plateaus of "bladed" terrains in the equatorial region, which rise 2-5 km above local terrains and are the highest standing geologic units on the encounter hemisphere. The mean elevations in the integrated DEM for the two radio occultation areas are consistent with the 5-6 km difference in elevation as determined independently by the radio experiment, and a limb profile near the egress point confirms the presence of elevated bladed terrains in that area. Local relief of 3-5 km at massifs, troughs and pits supports conclusions that the icy shell of Pluto is relatively rigid. Numerous examples of topographic control of ice or frost deposition occur across Pluto, including the distinct coloration of the polar dome, the elevated terrains of eastern Tombaugh Regio, and along the ridge-trough system, where ridge tops and fossae rims are covered in different ices than at lower elevations. The topographic hypsogram of Pluto's encounter hemisphere is strongly bimodal due to the large Sputnik Planitia depression. Otherwise the topographic signature of Pluto is controlled by deviations from the otherwise dominant low plains, including elevated bladed terrain plateaus and the depressed volcanic province including Wright and Piccard Montes.