Given a smooth cubic threefold $Y$, its intermediate Jacobian is a principally polarized abelian variety of dimension 5. Given a general cubic fourfold $X$, we can consider over the open subset $U$ of $\mathbb{P}^5$ that parameterizes smooth hyperplane sections of $X$, the universal family $Y_U \to U$ and its relative intermediate Jacobian $f: J_U \to U$. In 1995, Donagi and Markman constructed a holomorphic symplectic form on $J_U$, with respect to which the fibration $f$ is Lagrangian. Since then, there have been many attempts to find a smooth hyperkahler compactification $J$ of $J_U$, which was conjectured to exist and to be deformation equivalent to O’Grady’s 10-dimensional exceptional example. In joint work with R. Laza and C. Voisin, we solve this problem by using relative compactified Prym varieties to construct a natural smooth compactification of $J_U$ that admits a holomorphic symplectic form.