We compared the structure of two flat and two conical mud volcanoes (MV) in Azerbaijan in order to understand what governs the morphological contrast. We paid particular attention to the structural evolution of the surface, as observed in the field over 5 years and as monitored by satellite images revealing surface activity over that period; in addition, we acquired microgravity measurements to probe deeper structure. The combination of these data reveals in all studied volcanoes significant mass deficit concentric with the surface edifice. Modeling indicates that the mass deficit is consistent with a chamber underlying the summit caldera of conical MVs and the plateau of flat MVs, with a thickness of several hundred meters for a density contrast of 500 kg/m3 between the chamber mud and the surrounding solid mud. Surface structures and their evolution during and in between eruptions provide insight into the depth of the mud chamber, which lies within a few meters of the surface for flat mud volcanoes and one to several hundred meters deep for conical ones. Surface structures and satellite-derived deformation analysis shows that flat mud volcanoes grow by radial expansion and compression of the flanks distributed all around the edifice. In contrast, conical mud volcanoes grow by flow stacking in the summit caldera, deformation being constrained by the caldera rim; excess mud supply is accommodated by occasional rim breaching and mud overflow into flank gullies.