In this talk we will introduce exponential sums over finite fields and discuss how we can study them via Dwork Theory. Our focus will be on the $p$-adic Newton polygons of their $L$-functions and how these polygons behave in families of exponential sums. In particular, we utilize a new Dwork theory allowing us to compute the degree of the $L$-function and a lower bound for the Newton polygon (the Hodge polygon) in a previously unknown case.