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 that play a key role in understanding the dynamics of field theories.  These advances have rekindled a longstanding hope for a Landau paradigm in quantum field theory: a classification of possible long-distance behavior, based on patterns of symmetry realization in the vacuum.  I will review these ideas and selected applications in gauge theory.