  With the arrival of powerful, ground-based gamma-ray detectors, we can now
begin to seriously probe, via simultaneous X-ray/TeV observations, the origin
of the gamma-ray emission in the blazars Mrk 421 and 501. If the
synchrotron-Compton emission model turns out to work, then we know that the
same electrons are responsible for both the X-ray and the gamma-ray emission of
these objects. In this case, we show that we can use their observed X-ray
spectra to robustly estimate their intrinsic gamma-ray spectra. Among blazars,
Mrk 421/501 are particularly well-suited for this task because the Compton
scattering which produces their TeV gamma-rays is likely to be in the
Klein-Nishina limit, where the outgoing photon has an energy insensitive to the
incoming photon energy. With a better handle on their intrinsic TeV spectra, we
can then begin to search for evidence of absorption due to gamma-ray pair
production on diffuse infrared background radiation. We discuss some of the
pitfalls that arise when one attempts to do this without knowing the intrinsic
spectrum. Although Mrk 421/501 are very nearby, the emission of these sources
extends to sufficiently high energies (> 20 TeV in Mrk 501) that we may
nevertheless be able to derive interesting constraints on the infrared
background. If correct, the combination of the COBE 140 micron detection and
the measurement of Mrk 501's spectrum out to 20 TeV and perhaps beyond rules
out conventional galaxy evolution and star formation scenarios, implying that
much of the star formation in the Universe indeed occurs at early times in
highly obscured sources that have been missed until now.
