Extremal Combinatorics studies how large or how small a collection of finite objects can be, if it has to satisfy certain restrictions. In this talk, we will discuss how the eigenvalue interlacing method can be used to prove various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for hypercubes, and the resolution of the Sensitivity Conjecture.