||The mature human immunodeficiency virus type 1 (HIV-1), like other lentiviruses, contains a characteristic conical viral capsid at its center. The capsid is composed of ~1,500 copies of the viral CA protein, and is formed following assembly and processing of the Gag polyprotein in a process called "maturation." Proper capsid assembly appears essential for viral replication, as mutations that disrupt capsid assembly are invariably non-infectious. In vitro, HIV-1 CA can spontaneously assemble into helical tubes and cones that resemble the authentic viral capsid. Electron cryo-microscopy and image reconstructions revealed that the tubes assemble on a curved p6 lattice, where the repeat unit is a hexamer of CA molecules. Crystal structures of the two CA domains have been "docked" into the averaged reconstructed tube structure. The N-terminal domains form the hexameric rings and the C-terminal domains connect each ring to six neighbors. Our reconstructions have also revealed striking helical family polymorphism in CA assembly. In the light of the principle of quasi-equivalence, these observations, together with morphological studies of CA-NC cones formed in vitro, provide a molecular model for the HIV-1 capsid that follows the structural principles of a "fullerene cone." To understand determinants of capsid assembly, different forms of the CA protein and their in vitro assemblies were studied. This work revealed that the beta-hairpin structure at the N-terminus of CA protein helps to regulate the viral maturation transition. Fusing as few as four MA residues to the N-terminus of CA redirected the in vitro assembly of CA from tubes and cones to spheres. This change resembles the morphological change during viral maturation. Moreover, mutations that destabilize the beta-hairpin structure also disrupted CA assembly in vitro. Sequence analyses suggest that the "beta-hairpin switch" model can be applied generally to the maturation of other retroviruses.