I will attempt to partially answer some of the following questions: What is the Riemann zeta function and why is it important? What do zeros of zeta have to do with prime numbers? What is the Riemann hypothesis? Why would we like it to be true? I will give some history along the way, including a discussion of Riemann's epoch-making memoir \emph{On the number of primes less than a given magnitude}. No background is necessary.