Beyond the universality of the symmetry concept, there are different emphases on its application in different branches of science. Chemistry, being between particle physics and astrophysics, represents a bridge in, and a utilitarian approach to, the application of the symmetry concept, which has proved immensely fruitful in twentieth-century science. Some pivotal discoveries, especially in structural chemistry, molecular biology, and materials science, emerged by relaxing some of the stipulations of the classical teachings about symmetry. This highly personal presentation relies on ideas expressed by a number of notable individuals in recent science, among them J. Desmond Bernal, Francis Crick, Ronald J. Gillespie, Aleksandr I. Kitaigorodskii, Alan L. Mackay, George A. Olah, Linus Pauling, Roger Penrose, Dan Shechtman, James D. Watson, Steven Weinberg, and Eugene P. Wigner.