Observing high-energy gamma-rays from Active Galactic Nuclei (AGN) offers a unique potential to probe extremely tiny values of the intergalactic magnetic field (IGMF), a long standing question of astrophysics, astroparticle physics and cosmology. Very high energy (VHE) photons from blazars propagating along the line of sight interact with the extragalactic background light (EBL) and produce e+e− pairs. Through inverse-Compton interaction, mainly on the cosmic microwave background (CMB), these pairs generate secondary GeV-TeV components accompanying the primary VHE signal. Such secondary components would be detected in the gamma-ray range as delayed “pair echos” for very weak IGMF (B < 10−16G), while they should result in a spatially extended gamma-ray emission around the source for higher IGMF values (B > 10−16G). Coordinated observations with space (i.e. Fermi) and ground-based gamma-ray instruments, such as the present Cherenkov experiments H.E.S.S., MAGIC and VERITAS, the future Cherenkov Telescope Array (CTA) Observatory, and the wide-field detectors such as HAWC and LHAASO, should allow to analyze and finally detect such echos, extended emission or pair halos, and to further characterize the IGMF.