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The study of symmetry lies at the heart of various parts of physics. In equilibrium physics, symmetries are useful in classifying phases of matter and in non-equilibrium physics, they are necessary to understand the phenomenon of thermalization. Most symmetries conventionally studied in the literature are examples of so-called on-site unitary symmetries, which have a nice group structure. While such symmetries are sufficient to explain several physical phenomena, recent discoveries of dynamical phenomena collectively known as weak ergodicity breaking have called for a generalization of the notion of symmetry. In this talk, I will discuss the physics of weak ergodicity breaking, particularly phenomena known as quantum many-body scars and Hilbert space fragmentation, and how it motivates a general mathematical framework to define symmetries in quantum many-body systems based on von Neumann algebras. This framework leads to a generalization of the notion of symmetry beyond the conventional ones, provides precise explanation of weak ergodicity breaking in terms of unconventional symmetries, unifies the study of various different dynamical phenomena in the literature, and also opens up several questions on the nature of symmetry in quantum many-body physics.