Almost a century ago, in 1927, Emil Artin proposed a conjectural density for the set of primes p for which a given integer g is a primitive root mod p. Although elementary to state, Artin’s conjecture touches on deep aspects of algebraic number theory and arithmetic geometry. In this talk, I will trace the history of Artin’s conjecture and explain the heuristic behind it. I will then discuss how the problem evolves in the context of elliptic curves, and highlight how the ideas initiated by Artin continue to inspire some of the current research in number theory.