Hyperkahler manifolds are one of the main classes of manifolds appearing in Berger’s classification of holonomy groups of Riemannian manifolds. It is known that for any non-constant map f from a hyperkahler manifold of dimension 2n, the generic fibers of f are either finite or abelian varieties of dimension n. The latter are Lagrangian fibrations. I will discuss some open problems and some results concerning Lagrangian fibrations on hyperkahler manifolds.