Braid groups are fundamental objects in mathematics and categorification is the process of replacing set-theoretic theorems by category-theoretic analogues. We will connect the two by discussing a categorification of the Temperley-Lieb Algebra which results in a braid group action. We will conclude by discussing how a braid group action leads to a homology theory of links - triply graded link homology recently discovered by Mikhail Khovanov.