The modern study of a crowd as a flowing continuum is a recent development. Distinct from a classical fluid because of the property that a crowd has the capacity to think, interesting new physical ideas are involved in its study. An appealing property of a crowd in motion is that the nonlinear, time-dependent, simultaneous equations representing a crowd are conformably mappable. This property makes many interesting applications analytically tractable. In this review examples are given in which the theory has been used to provide possible assistance in the annual Muslim Hajj, to understand the Battle of Agincourt, and, surprisingly, to locate barriers that actually increase the flow of pedestrians above that when there are no barriers present. Modern developments may help prevent some of the approximately two thousand deaths that annually occur in accidents owing to crowding.The field of crowd motion, that is, the field of "thinking fluids," is an intriguing area of research with great promise.