HIV forms spherical, membrane-enveloped, pleomorphic virions, 1,000-1,500 Å in diameter, which contain two copies of its single-stranded, positive-sense RNA genome. Virus particles initially bud from host cells in a noninfectious or immature form, in which the genome is further encapsulated inside a spherical protein shell composed of around 2,500 copies of the virally encoded Gag polyprotein. The Gag molecules are radially arranged, adherent to the inner leaflet of the viral membrane, and closely associated as a hexagonal, paracrystalline lattice. Gag comprises three major structural domains called MA, CA, and NC. For immature virions to become infectious, they must undergo a maturation process that is initiated by proteolytic processing of Gag by the viral protease. The new Gag-derived proteins undergo dramatic rearrangements to form the mature virus. The mature MA protein forms a "matrix" layer and remains attached to the viral envelope, NC condenses with the genome, and approximately 1,500 copies of CA assemble into a new cone-shaped protein shell, called the mature capsid, which surrounds the genomic ribonucleoprotein complex. The HIV capsid conforms to the mathematical principles of a fullerene shell, in which the CA subunits form about 250 CA hexamers arrayed on a variably curved hexagonal lattice, which is closed by incorporation of exactly 12 pentamers, seven pentamers at the wide end and five at the narrow end of the cone. This chapter describes our current understanding of HIV's virion architecture and its dynamic transformations: the process of virion assembly as orchestrated by Gag, the architecture of the immature virion, the virus maturation process, and the structure of the mature capsid.