In spite of the breakthrough due to Freedman and Donaldson, the topology of 4-manifolds still remains mysterious. But if we consider certain fibering structures on 4-manifolds, such structures help us much to approach 4-manifolds with methods of geometric topology. I would like to talk about Lefschetz fibrations on 4-manifolds, history and merit of them, monodromy representations, some open problems, and the new development of "broken Lefschetz fibrations".