Our understanding of the structure of Saturn's rings has evolved steadily since their discovery by Galileo Galilei in 1610. With each advance in observations of the rings over the last four centuries, new structure has been revealed, starting with the recognition that the rings are a disk by Huygens in 1656 through discoveries of the broad organization of the main rings and their constituent gaps and ringlets to Cassini observations that indirectly reveal individual clumps of particles tens of meters in size. The variety of structure is as broad as the range in scales. The main rings have distinct characteristics on a spatial scale of 104 km that suggest dramatically different evolution and perhaps even different origins. On smaller scales, the A and C ring and Cassini Division are punctuated by gaps from tens to hundreds of kilometer across, while the B ring is littered with unexplained variations in optical depth on similar scales. Moons are intimately involved with much of the structure in the rings. The outer edges of the A and B rings are shepherded and sculpted by resonances with the Janus—Epimetheus coorbitals and Mimas, respectively. Density waves at the locations of orbital resonances with nearby and embedded moons make up the majority of large-scale features in the A ring. Moons orbiting within the Encke and Keeler gaps in the A ring create those gaps and produce wakes in the nearby ring. Other gaps and wave-like features await explanation. The largest ring particles, while not massive enough to clear a gap, produce localized propeller-shaped disturbances hundreds of meters long. Particles throughout the A and B rings cluster into strands or self-gravity wakes tens of meters across that are in equilibrium between gravitational accretion and Keplerian shear. In the peaks of strong density waves particles pile together in a cosmic traffic jam that results in kilometer-long strands that may be larger versions of self-gravity wakes. The F ring is a showcase of accretion and disruption at the edges of Saturn's Roche zone. Clumps and strands form and are disrupted as they encounter each other and are perturbed by close encounters with nearby Prometheus. The menagerie of structures in the rings reveals a system that is dynamic and evolving on timescales ranging from days to tens or hundreds of millions of years. The architecture of the rings thus provides insight to the origin as well as the long and short-term evolution of the rings.