Consider a situation where n gossips each know a scandal unknown to the others. The gossips can phone each other, and in a phone call two gossips share with each other every scandal they know. What is the minimum number of phone calls required before each gossip knows every scandal? This problem is known as the Gossip Problem. We will look at the Gossip Problem, its solution, and an algebraic structure related to the gossip problem, the gossip monoid.