Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are a leading platform for emerging quantum technologies. There is a growing need in the community to address challenges from rising circuit complexity to the development of novel qubits. To meet these needs, we require efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here, we overview the process of quantum circuit design and present recent results to this end. We introduce the energy-participation ratio (EPR) quantization of Josephson circuits, suitable for a diverse class of general superconducting circuits. Finally, we also introduce an open-source framework to unify superconducting qubit design tools – project Qiskit Metal – which aims to bring together experimentalists and theorists alike seeking to push the boundaries of quantum circuit theory and Hamiltonian analysis.