  The intergalactic magnetic field (IGMF) in cosmic voids can be indirectly
probed through its effect on electromagnetic cascades initiated by a source of
TeV gamma rays, such as blazars, a subclass of active galactic nuclei. Blazars
that are sufficiently luminous at TeV energies, "extreme TeV blazars", can
produce detectable levels of secondary radiation from inverse Compton
scattering of the electrons in the cascade, provided that the IGMF is not too
large. We reveiw recent work in the literature which utilizes this idea to
derive constraints on the IGMF for three TeV-detected blazars-1ES 0229+200, 1ES
1218+304, and RGB J0710+591, and we also investigate four other hard-spectrum
TeV blazars in the same framework. Through a recently developed detailed 3D
particle tracking Monte Carlo simulation code, incorporating all major effects
of QED and cosmological expansion, we research effects of major uncertainties
such as the spectral properties of the source, uncertainty in the intensity of
the UV - far IR extragalactic background light (EBL), under-sampled Very High
Energy (VHE; energy > 100 GeV) coverage, past history of gamma-ray emission,
source vs. observer geometry, and jet AGN Doppler factor. The implications of
these effects on the recently reported lower limits of the IGMF are thoroughly
examined to conclude that presently available data are compatible with a zero
IGMF hypothesis.
