The Malay Basin is a mature hydrocarbon province that is being re-assessed for CO2 storage. Selecting appropriate storage sites requires a comprehensive understanding of the structural and stratigraphic history of the basin, but previous studies of the basin have been limited to observations from either regional, 2D seismic lines or individual 3D seismic volumes. Here, we access and utilize a basin-wide (~40,000 km2) 3D seismic and well database to describe the structural and stratigraphic features of the basin, particularly those within the uppermost ~ 4 km (Oligocene to Recent), to gain new insights into the evolution of the basin. E-W transtensional rift basins first developed because of sinistral shear across a NW-SE strike-slip zone. The NW-SE basin morphology seen today was generated during the late Oligocene – early Miocene during which time dextral motion across marginal hinge zones created en-echelon antithetic, extensional faults and pull-apart basins, especially well preserved along the western margin of the basin. Collisional forces to the southeast during the early-middle Miocene resulted in shallowing of the basin, intermittent connection to the South China Sea and a cyclic depositional pattern during the Miocene. During the late Miocene, significant uplift of the basin resulted in a major unconformity with up to 4 km of erosion and exhumation in the southeast of the basin. In the centre and northwest region, the inversion of deeper E-W rifts resulted in the folding of Miocene sequences, and the formation of large anticlines parallel to the rift-bounding faults. The Pliocene-Pleistocene history is more tectonically quiescent, but some extensional faulting continued to affect the northwest part of the basin. Larger glacio-eustatic sea-level fluctuations during this time resulted in major changes in sedimentation and erosion on the Sunda Shelf, including the formation of a middle-Pliocene unconformity. These structural events have created a variety of hydrocarbon traps across the basin, of different ages, including transpressional anticlines, rollover anticlines and tilted fault blocks. Each of these has discrete and distinct trap elements, with important implications for their CO2 storage potential.