Abstract
We explore the similarities and differences between simple theoretical models developed to describe the quantum optical micromaser and Josephson-photonics devices. Whilst the micromaser has long been recognised as an important model for the dynamics of open quantum systems far from equilibrium, so-called Josephson-photonics devices are a recently developed form of superconducting quantum circuit in which the quantum transport of charges through a voltage-biased Josephson junction drives the production of photons in a microwave resonator.