The often called “Hawaian” and the “Canarian” hydrogeological behavior of volcanic islands, do not respond to two different conceptual models but one, based on hydrodynamics, climate and volcanic edifice genesis. There is a wide range of possibilities according to structure, age, state of erosion, and precipitation, but responding to the same hydrogeological principles. The hydrogeological conceptual model of single hot-spot intraplate volcano is the combination of a low permeability core, a more permeable cover and a transmissive apron around. These parts may be from sharply separated to a gradual and fluctuating transition. The core holds the compacted old volcanics, the dike zones and sometimes the upper part of the magmatic chamber and ocean floor. These materials are usually thermally and hydrothermally altered. This is a common feature, even if not visible when it is covered by recent volcanics and soils. The core may hold large collapse calderas, later filled by intra-caldera volcanics and erosion materials, plus the corresponding extra-caldera cover. This fill may constitute a high elevation aquifer if closed around or be reduced to a recharge area if open by large landslides or deep erosion. The cover receives the high altitude recharge and groundwater flows to the periphery. Depending on permeability, recharge and thickness, springs and streams appear. The water table may be shallow or up to several hundred meters. The apron, continuous or not, may be narrow or extensive. Water table aquifers are commonly found in it. In the lowest parts semi-confining and even flowing conditions may appear when fine sediments are deposited. This is for a single main volcano under ideal conditions. Reality is more complex as there may be more than one main volcano, separated or partially overlapping, with a wide spectrum of different cumulative structures, state of erosion, and very diverse climate conditions. Attending to local conditions, very different hydrogeological conceptual models can be proposed, often with great uncertainties due to lack of data. The alternative is just applying judiciously the concept of core, cover and apron, focusing on hydrodynamics, and adapting it to the local circumstances and observations. This approach makes easier the formulation of local hydrogeological conceptual models. In the case of rift islands, the above presented approach seems to holds. Andesitic islands in subduction zones are less known, but knowledge can be derived from large volcanoes in continental location. The core, cover and apron concept seem to explain observations, especially in the mountain-front situation of volcanoes and the filled up graven-like large asymmetrical calderas at the side. A possible main difference with respect basaltic volcanism is the important role of thick and extensive ignimbrite deposits, both in intra- and extra-caldera positions.