Two groups are elementarily equivalent if they cannot be distinguished by means of a first-order sentence (a mathematical statement in which every variable represents an element of a group). Sela gave a complete classification of torsion-free hyperbolic groups up to elementary equivalence; in particular, he proved that non-abelian free groups are elementarily equivalent, answering a famous question of Tarski. I will discuss generalisations of this result to hyperbolic groups with torsion, and to acylindrically hyperbolic groups.