  Asymptotic safety is a remarkable example when fruitful ideas borrowed from
statistical physics proliferate to high-energy physics. The concept of
asymptotic safety is tightly connected to fixed points (FPs) of the
renormalization-group (RG) flow, and generalize well-known asymptotic freedom
to a scale-invariant ultraviolet completion with non-vanishing interactions. In
this review, we discuss the key ideas behind asymptotic safety, a mechanism for
achieving it, and the conditions it imposes on general gauge-Yukawa field
theories. We also pay special attention to possible phenomenological
applications and provide an overview of standard model (SM) extensions
potentially exhibiting asymptotic safety.
