Classical novae are explosive transients generated by runaway nuclear
burning on the surfaces of white dwarfs accreting from hydrogen-rich
binary companions.  Despite their storied role in the history of
Astronomy, our understanding of novae remains surprisingly incomplete.
In the standard paradigm, all nova emission derives directly from
energy released by nuclear burning in the hot envelope of the white
dwarf. However, this picture has been challenged by the recent
discovery of luminous ~GeV gamma-ray emission by Fermi LAT coincident
with the optical emission from ~10 classical novae.  The gamma-rays
originate from relativistic particles, likely ions accelerated at
strong shocks internal to the nova ejecta, providing new insights into
the time-dependent properties of nova outflows and enabling them to be
used as laboratories to study particle acceleration in shocks.  The
high densities in the nova outflow imply their internal shocks are
"radiative" and hence susceptible to various instabilities (thermal,
thin-shell) that endow unique features to the shock-generated emission
and particle acceleration properties.  I will discuss the range of
shock signatures in novae covering the entire electromagnetic
spectrum, and the implications our new-found understanding of these
nearby "garden variety" transients for other (typically much rarer and
hence more distant) hypothesized shock-powered transients, such as
superluminous supernovae.