Let $n$ be a positive integer. For $q \in \{1, 2,\ldots, n\}$, we call $q$ a quadratic residue $\bmod{n}$ if there exists an integer $x$ such that $x^2 \equiv q \pmod{n}$; otherwise, we call $q$ a quadratic non-residue $\bmod{n}$. We will discuss progress on the problem of finding how big the least quadratic non-residue can be. We will also discuss progress on bounding the least inert prime in a real quadratic field.