  Over the past decade, our knowledge of the \gamma-ray sky has been
revolutionized by ground- and space-based observatories by detecting photons up
to several hundreds of tera-electron volt (TeV) energies. A major population of
the $\gamma$-ray bright objects are active galactic nuclei (AGN) with their
relativistic jets pointed along our line-of-sight. Gamma-ray emission is also
detected from nearby mis-aligned AGN such as radio galaxies. While the
TeV-detected radio galaxies (TeVRad) only form a small fraction of the
\gamma-ray detected AGN, their multi-wavelength study offers a unique
opportunity to probe and pinpoint the high-energy emission processes and sites.
Even in the absence of substantial Doppler beaming TeVRad are extremely bright
objects in the TeV sky (luminosities detected up to 10^{45} erg/s), and exhibit
flux variations on timescales shorter than the event-horizon scales (flux
doubling timescale less than 5 minutes). Thanks to the recent advancement in
the imaging capabilities of high-resolution radio interferometry (millimeter
very long baseline interferometry, mm-VLBI), one can probe the scales down to
less than 10 gravitational radii in TeVRad, making it possible not only to test
jet launching models but also to pinpoint the high-energy emission sites and to
unravel the emission mechanisms. This review provides an overview of the
high-energy observations of TeVRad with a focus on the emitting sites and
radiation processes. Some recent approaches in simulations are also sketched.
Observations by the near-future facilities like Cherenkov Telescope Array,
short millimeter-VLBI, and high-energy polarimetry instruments will be crucial
for discriminating the competing high-energy emission models.
