Universal dynamics associated with scale-invariant properties has garnered much attention in the field of statistical mechanics for a long time. Thanks to the high controllability of ultracold atom experiments, such universal quantum dynamics has been studied theoretically and experimentally over a decade from the perspective of nonthermal fixed points, which was originally introduced in the context of high-energy physics. In this talk, we will begin with an introduction to ultracold atoms, reviewing applications of nonthermal fixed points to ultracold atoms by showing recent theoretical and experimental achievements.