Abstract: The demand for rapid and high-fidelity execution of initialization, gate and read-out operations casts tight constraints on the accuracy of quantum electrodynamic modeling of superconducting integrated circuits. In particular, radiative corrections to the properties of superconducting qubits, such as their transition frequency (Lamb shift) and the radiative decay rate (Purcell rate) have to be calculated to a high accuracy. In the pursuit of attaining the required accuracies we have found ourselves facing problems with divergent series akin to those that have plagued the original quantum electrodynamics of a single electron in free space. Interestingly, a semiclassical formulation of the Purcell rate is found to provide finite and accurate results. The reconciliation of the quantum and semiclassical results requires the reconsideration of our basic approach to the quantization of the electromagnetic field in a light-confining medium and the notion of normal modes. I will discuss a theoretical framework based on the Heisenberg-Langevin approach to address these fundamental questions. This framework allows the accurate computation of the quantum dynamics of a superconducting qubit in an arbitrarily complex electromagnetic environment and free of divergences that have plagued earlier approaches. I will also discuss the effectiveness of this computational approach in meeting the demands of present-day quantum computing research.