malle's conjecture can be thought of as a generalization of the inverse galois problem, which asks for every finite group $g$, is there a number field $k$ such that their galois group over $\mathbb{q}$ is isomorphic to $g$? although open, this question is widely believed to be true, and malle went further to predict the asymptotics of how many number fields there are with a given galois group that only depended on the group structure of $g$ and the degree of the number field. in this talk, we will discuss the history as well as recent results and techniques surrounding these conjectures.