Although there is general agreement that systematic variations of composition, temperature, and crystallinity in pyroclastic deposits provide strong evidence for chemical heterogeneities inside of magma chambers, no hypothesis for the origin of these heterogeneities is widely accepted. The chemical boundary layer flow hypothesis receives the most attention in the literature, but other potentially valuable hypotheses are ignored. In this paper, we review the representative hypotheses and attempt to quantitatively evaluate their potential for producing compositional heterogeneities. Our conclusions can be summarized as follows. Based on volcanological data for compositionally zoned eruptions, evolved magma is generated at a rate between 10-2 and 10-4 km3/a with a typical value of ∼10-3 km3/a. Melting of silicic country rock by intrusion of basaltic magma is a viable hypothesis because evolved melt is produced at a rate consistent with the volcanological observations. Some systems, however, do not show the extensive isotopic contamination predicted by this model. Mechanisms which involve porous media flow (separation of partial melts from the source region and boundary layers in a magma chamber's marginal liquid-crystal mush) are unlikely due to low permeability of the porous media. Diffusion-limited chemical boundary layers are capable of transporting significant quantities of H2O-rich melt to the roof of a magma chamber. Components which diffuse more slowly (for example, SiO2) are transported in sufficient quantities only if diffusively coupled to more mobile species in the melt. Cross-coupling effects will be important if the off-diagonal diffusion coefficients are 10% of the on-diagonal coefficients or larger.