  During the past few years, first observations of starburst galaxies at >GeV
energies could be made with the Fermi Gamma-ray Space Telescope (GeV range) and
Imaging Air Cherenkov Telescopes (TeV range). The two nearest starbursts, M82
and NGC253 were detected, and most recently, the detection of two
starburst-Seyfert composites (NGC1068 and NGC4945) were reported. The emission
for the two starbursts is best explained by hadronic interactions, and thus
providing a first, unique opportunity to study the role of cosmic rays in
galaxies. In this paper, the role of cosmic rays for the non-thermal component
of galaxies is reviewed by discussing the entire non-thermal frequency range
from radio emission to TeV energies. In particular, the interpretation of radio
emission arising from electron synchrotron radiation is predicted to be
correlated to TeV emission coming from interactions of accelerated hadrons.
This is observed for the few objects known at TeV energies, but the correlation
needs to be established with significantly higher statistics. An outlook of the
possibility of tracing cosmic rays with molecular ions is given.
