Lagrangian fibered Hyper-K\"ahler manifolds are the natural
generalization of elliptic K3 surfaces and have been used to study
and construct examples of compact Hyper-K\"ahler manifolds and
(possibly singular) symplectic varieties. In this talk I will talk
about some compactification techniques I introduced for
quasi-projective Lagrangian fibrations, with applications to the study
of Prym, Intermediate Jacobian, Albanese, dual fibrations etc.