Solid propellants are energetic materials used to launch and propel rockets and missiles. Although their history dates to the use of black powder more than two millennia ago, greater performance demands and the need for insensitive munitions that are resistant to accidental ignition have driven much research and development over the past half-century. The focus of this review is the material aspects of propellants, rather than their performance, with an emphasis on the polymers that serve as binders for oxidizer particles and as fuel for composite propellants. The prevalent modern binders are discussed along with a discussion of the limitations of state-of-the-art modeling of composite motors.