The topography of Piton de la Fournaise volcano (PdF) differs from the classic view of basaltic shield volcanoes as it is characterized by (1) several steep slope zones on its flanks and (2) a large U-shaped caldera, the Enclos-Grand Brûlé structure (EGBS). Most of these structures were previously interpreted as the scars of lateral landslides, the deposits of which cover the submarine flanks of PdF. We carried out a detailed analysis of the morphology of PdF, which reveals that the steep slope zones form two independent, circumferential structures that continue into the caldera. The development of circumferential steep slopes on volcano flanks may have several origins: constructive, destructive, and deformation processes. We interpret those processes acting on PdF as caused by the spreading of the volcanic edifice above a weak hydrothermal core, leading to outward displacements and a summit extensive stress field. The continuity of the steep slope on both sides of the EGBS escarpments suggests that this structure was not caused by a 4.5 ka old giant landslide as it is usually proposed but is due to a mainly vertical collapse. The recent debris avalanche deposits east of the island indicate that this event likely destabilized part of the submarine flank. We propose that the collapse of the Grand Brûlé, the lower half of the EGBS, was due to the downward drag related to the dense intrusive complex of the Alizés volcano, which is located 1 km below the Grand Brûlé. The collapse of the Enclos is interpreted as the consequence of the deformation of the hydrothermal system of the pre-Enclos volcano. Although the continuity of the geological and morphological structures between the Enclos and the Grand Brûlé suggests a narrow link between these two collapse events, their chronology and relationship are still uncertain. Finally, we hypothesize that the persistence of the NE and SE rift zones during the last 150 ka, despite the large changes of the topography related to the recurrent flank destabilizations, is linked to a deep sources, which can be either underlying crustal faults or the continuous downward subsidence of the Alizés intrusive complex.