As Hawaiian volcanoes develop, their lavas systematically change in composition and isotopic ratios of Sr, Nd and Pb. These trends provide important constraints for understanding plume-related volcanism as a volcano migrates away from the hotspot. There are also geochemical differences between Hawaiian shields. In particular, lavas from adjacent shields such as Kilauea and Mauna Loa on Hawaii and Koolau and Waianae on Oahu have significant differences in abundances of some major and incompatible elements and isotopic ratios of Sr, Nd and Pb. Some incompatible element abundance ratios, such as Zr/Nb and Sr/Nb, are correlated with intershield differences in Sr and Nd isotope ratios, but these isotopic ratios are not correlated with intershield differences in major element composition, or even parent/daughter abundance ratios such as Rb/Sr and Sm/Nd. Moreover, at Kilauea and Mauna Loa the intershield differences have apparently persisted for a relatively long time, perhaps 100 ka. These intershield geochemical differences provide important constraints on plume volcanism. Specifically, (i) each volcano must have distinct magma ascent paths from the region of melt segregation; (ii) the 25-50 km distance between adjacent, but geochemically distinct, shields requires that the sources vary on a similar scale, and that the melt production region is similarly restricted. The absence of correlations between lava compositions and radiogenic isotope ratios provides evidence for significant differences in melting process such as each shield forming by a different mean extent of melting with melt segregation at different mean pressures. Two types of models are consistent with the intershield geochemical differences: (i) a relatively large radius, ca. 40 km, plume conduit with a systematic spatial distribution of geochemical heterogeneities; or (ii) a small radius, less than 20 km, plume conduit composed of geochemically distinct diapirs. Because relatively small radius diapirs of limited vertical extent are too small to create the large Hawaiian shields, a possible alternative is a continuous conduit containing solitary waves which transport geochemically distinct packets of material.