  The performance of superconducting circuits for quantum computing is limited
by materials losses. In particular, coherence times are typically bounded by
two-level system (TLS) losses at single photon powers and millikelvin
temperatures. The identification of low loss fabrication techniques, materials,
and thin film dielectrics is critical to achieving scalable architectures for
superconducting quantum computing. Superconducting microwave resonators provide
a convenient qubit proxy for assessing performance and studying TLS loss and
other mechanisms relevant to superconducting circuits such as non-equilibrium
quasiparticles and magnetic flux vortices. In this review article, we provide
an overview of considerations for designing accurate resonator experiments to
characterize loss, including applicable types of loss, cryogenic setup, device
design, and methods for extracting material and interface losses, summarizing
techniques that have been evolving for over two decades. Results from
measurements of a wide variety of materials and processes are also summarized.
Lastly, we present recommendations for the reporting of loss data from
superconducting microwave resonators to facilitate materials comparisons across
the field.
