In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This article explores how the authors have used both to help students see the mathematics in their tennis game. The problems and activities also help answer the question they frequently hear: "When are we ever going to use this stuff?" Although this article focuses exclusively on connecting mathematics and tennis, other sports--such as football, soccer, baseball, and basketball--and their specific playing surfaces can provide rich environments for making mathematical connections. (Contains 10 figures.)