Abstract: "Despite the high measurement fidelity that can now be reached, the dispersive qubit readout of circuit QED is not as good as we expected. As we increase the measurement strength, there is a point beyond which the fidelity drops and the qubit state is demolished. In this talk, we focus on the transmon qubit and discuss a comprehensive framework that explains why the transmon “ionizes” during dispersive readout. This framework consists of three complementary levels of descriptions: a fully quantized transmon-resonator model, a semiclassical model where the resonator is treated as a classical drive on the transmon, and a fully classical model. All three approaches lead to similar predictions, which, crucially, agree with experimental results. This framework identifies the multiphoton resonances responsible for transmon ionization. It also allows for the efficient computation of numerical estimates of the photon number threshold for ionization. We will briefly discuss how these analyses might help us understand the limitations in the measurements of other qubits and other types of qubit operations."