Abstract: Symmetry is a powerful mathematical tool for organizing physical phenomena and anchors our understanding of the laws of nature. Over the past century, the theory of symmetry has evolved in parallel with quantum physics and has become fundamentally intertwined with quantum field theory and topology. Recently, new generalized concepts of symmetry have been developed and rekindled a longstanding hope for a classification of phases of field theories based on patterns of symmetry realization in the vacuum. These novel symmetries may also play a role in addressing long-standing mysteries of particle physics, such as hierarchies in the masses and couplings of elementary particles. I will survey these developments and applications.