Let $f$ be an holomorphic function with an essential singularity at $w\in \mathbb{C}$ Then there is a number $z_0\in \mathbb{C}$ such that the image of any neighborhood of $w$ by $f$ contains $\mathbb{C}-\{z_0\}$ In other words, $f$ assumes every complex value, with the possible exception of $z_0$ in any neighborhood of $w$

Remark. Little Picard theorem follows as a corollary: Given a nonconstant entire function $f$ if it is a polynomial, it assumes every value in $\mathbb{C}$ as a consequence of the fundamental theorem of algebra. If $f$ is not a polynomial, then $g(z)=f(1/z)$ has an essential singularity at $0$ Picard's theorem implies that $g$ (and thus $f$ assumes every complex value, with one possible exception.