Asymptotic safety generalizes asymptotic freedom and could contribute to
understanding physics beyond the Standard Model. It is a candidate scenario to
provide an ultraviolet extension for the effective quantum field theory of
gravity through an interacting fixed point of the Renormalization Group.
Recently, asymptotic safety has been established in specific gauge-Yukawa
models in four dimensions in perturbation theory, providing a starting point
for asymptotically safe model building. Moreover, an asymptotically safe fixed
point might even be induced in the Standard Model under the impact of quantum
fluctuations of gravity in the vicinity of the Planck scale. This review
contains an overview of the key concepts of asymptotic safety, its application
to matter and gravity models, exploring potential phenomenological implications
and highlighting open questions.Comment: minor changes, references added; version identical with published on
