The classification problem has always played a central role in algebraic geometry. To address it, one studies invariants—quantities that describe intrinsic properties of a variety and remain unchanged under suitably well-behaved maps. For curves (that is, one-dimensional varieties), a classical and well-known invariant is the Clifford index, which measures how far a curve is from being hyperelliptic, i.e., a double cover of P^1. In this seminar, I will introduce the Clifford index and discuss its main properties and results, aiming to convey a geometric intuition. Finally, I will mention a work in progress about the definition of a new invariant, the Prym-canonical Clifford index.