The simplicity of hard spheres as a model system is deceptive. Although the particles interact solely through volume exclusion, that nevertheless suffices for a wealth of static and dynamical phenomena to emerge, making the model an important target for achieving a comprehensive understanding of matter. In addition, while real colloidal suspensions are typically governed by complex interactions, Pusey and Van Megen [Nature 320 340–342 (1986)] demonstrated that suitably tuned suspensions result in hard-sphere like behavior, thus bringing a valuable experimental complement to the celebrated theoretical model. Colloidal hard spheres are thus both a material in their own right and a platform upon which phenomena exhibited by simple materials can be explored in great detail. These various purposes enable a particular synergy between experiment, theory and computer simulation. Here we review the extensive body of work on hard spheres, ranging from their equilibrium properties such as phase behavior, interfaces and confinement to some of the non–equilibrium phenomena they exhibit such as sedimentation, glass formation and nucleation