We review evidence regarding the origin of material accelerated in large, gradual solar energetic particle (SEP) events. According to the two-class paradigm in place at the start of solar cycle 23, impulsive SEP events accelerate heated flare material, while gradual SEP events are accelerated out of the solar wind by shocks driven by fast coronal mass ejections (CMEs). However, new data from solar cycle 23 has shown that the energetic ions in gradual events often include composition signatures associated with impulsive events, including emichments in 3 He, heavy elements such as Fe, and ionic charge states indicative of~ 10 MK temperatures. In addition, gradual SEP events differ in composition from bulk solar wind in several key respects, implying that solar wind is not the principal seed population for these events. Several lines of evidence show that CME-driven shocks accelerate principally suprathennal ions with velocities several times that of the solar wind. The suprathermal pool incorporates ions from impulsive solar flares and previous gradual events, CIR events, pickup ions, CME ejecta, and the suprathermal tail of the solar wind. This paper reviews evidence for the sources of ions accelerated in gradual SEP events, considers the composition and available densities of suprathermal ions, and describes models that attempt to account for the surprisingly variable composition of gradual SEP events. We find that below ~1 MeV/nucleon almost all events are Fe-rich compared to the average 5 to 12 MeV/nucleon SEP composition. Iron-rich SEP events above 10 Me V /nucleon occur mainly dming periods when the intensity of suprathermal iron in the inner heliosphere is high, due mainly to previous gradual events.