The Weil Conjectures are one of the most beautiful theorems in mathematics. In the number field context zeta and L-functions are transcendental. It is well known, for example, that zeta(2)=pi^2/6. The values of these functions, even at integers, are not well understood. The Weil conjectures state the perhaps shocking result that the function field analogues of these functions are almost as simple as possible: they are rational functions. Further, they include the analogue of the Riemann Hypothesis for function fields. In this talk we will explore what the Weil conjectures say, as well as how they are proven.