Large volcanic provinces are traditionally attributed to plumes of hot material rising from the core-mantle boundary. However, with ever-improving quantity and quality of data, there is growing awareness that the most fundamental predictions of the plume model are often not confirmed by observation. At well-studied areas such as Iceland and Yellowstone, multiple predictions of plume theory may be tested. Evidence for high, plume-like temperatures is absent in petrology and heat flow. At Iceland, and most other hotspots, there is no hotspot track. Volcanism there has always coincided with the mid-Atlantic ridge, and has not migrated as predicted by models of relative hotspot fixity. The mantle low-velocity anomaly extends no deeper than the mantle transition zone. At Yellowstone, superimposed on widespread basaltic volcanism, there is a time-progressive track of silicic volcanism that has an orientation consistent with the fixed-hotspot reference frame. However, there, the mantle seismic low-velocity anomaly clearly does not extend deeper than ~ 200 km, arguing against a downward-continuous plume. In both regions, high maximum values of helium isotope ratios are observed, generally assumed to indicate plume-transported, lower-mantle material. Other observations, however, are incompatible with either Iceland or Yellowstone being the products of deep mantle plumes, suggesting that voluminous melt, time-progressive volcanic tracks, high helium isotope ratios and OIB geochemistry may result from shallow processes. Such observations may thus not be used as conclusive evidence for plumes elsewhere. Alternative theories can explain the holistic observations at volcanic provinces with less special pleading and fewer coincidences than the plume model. Excess melt may be produced by variations in fertility, e.g., remelting recycled oceanic crust in old subduction zones and sutures. This is predicted to generate much greater volumes of melt than passive upwelling, and can also explain OIB geochemistry. Local EDGE convection, and melt focusing at the juxtaposition of thick cratons and thin, young crust, also predict anomalous melt volumes and can explain volcanic margins. High helium-isotope ratios may be preserved by storage of ancient helium in low U, Th rocks, e.g., the mantle lithosphere, and time progressive magmatism may result from the propagation of cracks where intraplate extensional strain gradients exist. Large volcanic provinces clearly have various genesis mechanisms, and cannot all be attributed to one cause. Alternative theories must be critically discussed as part of the work of data interpretation and should take precedence over plume models where they are more consistent with the observations as a whole.