The rise of quantum information science has provided new perspectives on quantum mechanics, as well as a common language for quantum engineering. The focus on platforms for the manipulation and processing of quantum information bridges between different research areas in physics as well as other disciplines. Such a crossover between borders is well embodied by the development of hybrid quantum systems, where heterogeneous physical systems are combined to leverage their individual strengths for the implementation of novel functionalities. In the microwave domain, the hybridization of various quantum degrees of freedom has been tremendously helped by superconducting quantum circuits, owing to their large zero-point field fluctuations, small dissipation, strong nonlinearity and design flexibility. These efforts take place by expanding the framework of circuit quantum electrodynamics. Here, we review recent research on the creation of hybrid quantum systems based on circuit quantum electrodynamics, encompassing mechanical oscillators, quantum acoustodynamics with surface acoustic waves, quantum magnonics and coupling between superconducting circuits and ensembles or single spins.