Abstract: I will begin by discussing how and when the action of a Hopf algebra $H$ on an algebra $A$ can be viewed as a grading of $A$. For example, if $G$ is a finite group and $H$ is the dual of the group algebra $K[G]$, then $A$ is an $H$-algebra precisely when $A$ is group-graded by $G$. I will then discuss the identical relations of an algebra with a Hopf algebra action. In particular, I will address the following question: when does the existence of an $H$-identity on $A$ imply the existence of an ordinary polynomial identity on $A$?