Given a system of polynomial equations $P_1=P_2=⋯=P_n=0$, one naturally asks about the existence and distribution of rational solutions. The answer turns out to depend intimately on the geometry of the variety defined by these equations. For instance, by Faltings' theorem, a curve of genus at least 2 admits only finitely many rational points. In contrast, a genus-zero curve with even a single rational point is isomorphic to the projective line, and thus has infinitely many. Manin's conjecture predicts the asymptotic growth of rational points of bounded "arithmetic size" on certain Fano varieties—those expected to have "many" rational solutions. In this talk, we explore the conjecture and present some recent developments.