  Hydrodynamical shocks are a manifestation of the non-linearity of the Euler
equations and play a fundamental role in cosmological gas dynamics. In this
work, we identify and analyse shocks in the Illustris simulation, and contrast
the results with those of non-radiative runs. We show that simulations with
more comprehensive physical models of galaxy formation pose new challenges for
shock finding algorithms due to radiative cooling and star-forming processes,
prompting us to develop a number of methodology improvements. We find in
Illustris a total shock surface area which is about 1.4 times larger at the
present epoch compared to non-radiative runs, and an energy dissipation rate at
shocks which is higher by a factor of around 7. Remarkably, shocks with Mach
numbers above and below $\mathcal{M}\approx10$ contribute about equally to the
total dissipation across cosmic time. This is in sharp contrast to
non-radiative simulations, and we demonstrate that a large part of the
difference arises due to strong black hole radio-mode feedback in Illustris. We
also provide an overview of the large diversity of shock morphologies, which
includes complex networks of halo-internal shocks, shocks on to cosmic sheets,
feedback shocks due to black holes and galactic winds, as well as ubiquitous
accretion shocks. In high redshift systems more massive than
$10^{12}\,\mathrm{M}_\odot$ we discover the existence of a double accretion
shock pattern in haloes. They are created when gas streams along filaments
without being shocked at the outer accretion shock, but then forms a second,
roughly spherical accretion shock further inside.
