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Thermodynamic systems typically conserve quantities (known as charges) such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on the failure of observables to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Noncommutation of charges has been found to invalidate derivations of the form of the thermal state, decrease entropy production, conflict with the eigenstate thermalization hypothesis and more. This Perspective surveys key results in, opportunities for and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.