  Performance of superconducting resonators, particularly cavities for particle
accelerators and micro cavities and thin film resonators for quantum
computations and photon detectors has been improved substantially by recent
materials treatments and technological advances. As a result, the niobium
cavities have reached the quality factors $Q\sim 10^{11}$ at 1-2 GHz and 1.5 K
and the breakdown radio-frequency (rf) fields $H$ close to the dc superheating
field of the Meissner state. These advances raise the question whether the
state-of-the-art cavities are close to the fundamental limits, what these
limits actually are, and to what extent the $Q$ and $H$ limits can be pushed by
the materials nano structuring and impurity management. These issues are also
relevant to many applications using high-Q thin film resonators, including
single-photon detectors and quantum circuits. This topical review outlines
basic physical mechanisms of the rf nonlinear surface impedance controlled by
quasiparticles, dielectric losses and trapped vortices, as well as the dynamic
field limit of the Meissner state. Sections cover ways of engineering an
optimum quasiparticle density of states and superfluid density to reduce rf
losses and kinetic inductance by pairbreaking mechanisms related to magnetic
impurities, rf currents, and proximity-coupled metallic layers at the surface.
A section focuses on mechanisms of residual surface resistance which dominates
rf losses at ultra low temperatures. Microwave losses of trapped vortices and
their reduction by optimizing the concentration of impurities and pinning
potential are also discussed.
