Global symmetry is a key factor in determining the universality class of the long-distance, low-energy physics for quantum many-body systems. In recent years, it has been appreciated that unlocking the full power of symmetry requires the study of topological defect operators. I will discuss how measuring the “disorder parameter”, the expectation value of a defect operator, provide new probes into quantum phases of matter. I will illustrate the use of disorder parameter with two examples in (2+1)d: (1) in gapped insulators, where measuring exponentiated electric charge inside a region reveals topological invariants of the ground state, and (2) at quantum critical points, disorder parameters receive logarithmic corrections, whose universal coefficients can be used to characterize the quantum criticality.