Everybody knows that Fermat's Last Theorem is actually a theorem, proved by Andrew Wiles. What is less well known is that what Wiles actually proved is the Taniyama-Shimura conjecture for "elliptic curves with semistable reduction." First, I will explain the statement of the Taniyama-Shimura conjecture in terms of modular forms viewed as complex-analytic objects. Next, I will move to the arithmetic setting, and explain how the Taniyama-Shimura conjecture is actually an statement about varieties over $\mathbb{Q}$. Finally, I will discuss the relationship between modular forms, elliptic curves and Galois representations, and say a word or two about Wiles' proof.