The crustal structure of the Equatorial Atlantic conjugate margins (South America and West Africa) has been investigated using 3D gravity anomaly inversion, which allows for (1) the elevated geothermal gradient of the lithosphere following rifting and break-up and (2) magmatic addition to the crust during rifting and break-up. It is therefore particularly suitable for the analysis of rifted margins and their associated ocean basins. Maps of crustal thickness and conjugate-margin stretching, derived from gravity anomaly inversion, are used to illustrate how the Equatorial Atlantic opened as a set of stepped rift-transform segments, rather than as a simple orthogonal rifted margin. The influence of the transform faults and associated oceanic fracture zones is particularly clear when the results of the gravity anomaly inversion are combined with a shaded-relief display of the free-air gravity anomaly. A set of crustal cross-sections has been extracted from the results of the gravity inversion along both equatorial margins. These illustrate the crustal structure of both rifted-margin segments and transform-margin segments. The maps and cross-sections are used to delineate crustal type on the margins as (1) inboard, entirely continental, (2) outboard, entirely oceanic and (3) the ocean-continent transition in between where mixed continental and magmatic crust is likely to be present. For a given parameterization of melt generation the amount of magmatic addition within the ocean-continent transition is predicted by the gravity inversion. One of the strengths of the gravity-inversion technique is that these predictions can be made in the absence of any other directly acquired data. On both margins anomalously thick crust is resolved close to a number of oceanic fracture zones. On the South American margin we believe that this thick crust is probably the result of post-break-up magmatism within what was originally normal-thickness oceanic crust. On the West African margin, however, three possible origins are discussed: (1) continental crust extended oceanwards along the fracture zones; (2) oceanic crust magmatically thickened at the fracture zones; and (3) oceanic crust thickened by transpression along the fracture zones. Gravity inversion alone cannot discriminate between these possibilities. The cross-sections also show that, while 'normal thickness' oceanic crust (c. 7 km) predominates regionally, local areas of thinner (c. 5 km) and thicker (c. 10 km) oceanic crust are also present along both margins. Finally, using maps of crustal thickness and thinning factor as input to plate reconstructions, the regional palaeogeography of the Equatorial Atlantic during and after break-up is displayed at 10 Ma increments.Supplementary material: Detailed illustrations of the crustal-thickness mapping, the crustal cross-sections and the plate reconstructions are available at: https://doi