The recent evidences for the presence of the Extragalactic magnetic fields (EGMF) from the gamma-ray observations of distant blazars have started an ongoing debate about the role the electromagnetic cascades play in the extragalactic space. With the lower bound on the strength of the EGMF at the level of 10-17}G, these fields could have served as seeds for the magnetic fields now present in galaxies and their clusters. However, the origin of the EGMF is largely uncertain. Here I review the current state of the observational constraints on the EGMF, as well as different theoretical scenarios, in which they could have formed, and give some prospects for the future space and ground-based gamma-ray instruments.