The structure of the HIV-1 capsid is analysed by cryo-electron microscopy and cryo-electron tomography, allowing presentation of an all-atom molecular dynamics model of the entire capsid. Human immunodeficiency virus-1 (HIV-1), the predominant AIDS virus, contains a spheroidal capsid enclosing the viral RNA genome. As the retrovirus matures, the capsid forms through spontaneous oligomerization of the capsid protein CA. Using cryo-electron microscopy and cryo-electron tomography, combined with all-atom large-scale molecular dynamics simulations, Gongpu Zhao et al. have determined a complete atomic structure of the HIV-1 capsid. The resulting structural models reveal elements that are essential for capsid formation, stability and viral infectivity. Of special interest are the hydrophobic interactions evident in a novel three-fold interface between the carboxy-terminal domains of CA protein, a feature that appears to be unique to the mature capsid and which has previously been suggested as a potentially attractive therapeutic target. Retroviral capsid proteins are conserved structurally but assemble into different morphologies1. The mature human immunodeficiency virus-1 (HIV-1) capsid is best described by a ‘fullerene cone’ model2,3, in which hexamers of the capsid protein are linked to form a hexagonal surface lattice that is closed by incorporating 12 capsid-protein pentamers. HIV-1 capsid protein contains an amino-terminal domain (NTD) comprising seven α-helices and a β-hairpin4,5, a carboxy-terminal domain (CTD) comprising four α-helices6,7, and a flexible linker with a 310-helix connecting the two structural domains8. Structures of the capsid-protein assembly units have been determined by X-ray crystallography9,10; however, structural information regarding the assembled capsid and the contacts between the assembly units is incomplete. Here we report the cryo-electron microscopy structure of a tubular HIV-1 capsid-protein assembly at 8 Å resolution and the three-dimensional structure of a native HIV-1 core by cryo-electron tomography. The structure of the tubular assembly shows, at the three-fold interface11, a three-helix bundle with critical hydrophobic interactions. Mutagenesis studies confirm that hydrophobic residues in the centre of the three-helix bundle are crucial for capsid assembly and stability, and for viral infectivity. The cryo-electron-microscopy structures enable modelling by large-scale molecular dynamics simulation, resulting in all-atom models for the hexamer-of-hexamer and pentamer-of-hexamer elements as well as for the entire capsid. Incorporation of pentamers results in closer trimer contacts and induces acute surface curvature. The complete atomic HIV-1 capsid model provides a platform for further studies of capsid function and for targeted pharmacological intervention.