The spectra of many X-ray pulsars show , in addition to a power law , a low-energy component that has often been modeled as a blackbody with kT _ { BB } \sim 0.1 keV . However the physical origin of this soft excess has remained a mystery . We examine a sample of well-studied , bright X-ray pulsars , which have been observed using ROSAT , ASCA , Ginga , RXTE , BeppoSAX , Chandra , and XMM-Newton . In particular , we consider the Magellanic Cloud pulsars SMC X-1 , LMC X-4 , XTE J0111.2–7317 , and RX J0059.2–7138 and the Galactic sources Her X-1 , 4U 1626–67 , Cen X-3 , and Vela X-1 . We show that the soft excess is a very common if not ubiquitous feature intrinsic to X-ray pulsars . We evaluate several possible mechanisms for the soft emission , using theoretical arguments as well as observational clues such as spectral shapes , eclipses , pulsations of the soft component , and superorbital modulation of the source flux . We find that reprocessing of hard X-rays from the neutron star by the inner region of the accretion disk is the only process that can explain the soft excess in all the pulsars with L _ { X } \gtrsim 10 ^ { 38 } ergs s ^ { -1 } . Other mechanisms , such as emission from diffuse gas in the system , are important in less luminous objects .