  Events with vector bosons produced in association with jets have been
extensively studied at hadron colliders and provide high-accuracy tests of the
Standard Model. A good understanding of these processes is of paramount
importance for precision Higgs physics, as well as for searches for new
physics. In particular, associated production of $\gamma$, $W$ or $Z$ bosons
with light-flavor and heavy-flavor jets is a powerful tool for testing
perturbative QCD calculations, Monte Carlo event generators, and can also
constrain the parametrizations used to describe the parton content of the
proton. Furthermore, events with a $W$ or $Z$ boson produced with two
well-separated jets can be used to distinguish between electroweak and strong
production mechanisms, and to set limits on contributions of physics beyond the
Standard Model. This review summarises the historical theoretical developments
and the state-of-the-art in the modeling of vector-boson-plus-jet physics,
while focusing on experimental results by LHC collaborations in Run-1 and
Run-2, and including comparisons with recent measurements at the Tevatron.
