  The production of both charged and neutral electroweak gauge bosons in
association with $b$ jets has attracted a lot of experimental and theoretical
attention in recent years because of its central role in the physics programs
of both the Fermilab Tevatron and the CERN Large Hadron Collider. The improved
level of accuracy achieved both in the theoretical predictions and experimental
measurements of these processes can promote crucial developments in modeling
$b$-quark jets and $b$-quark parton distribution functions, and can provide a
more accurate description of some of the most important backgrounds to the
measurement of Higgs-boson couplings and several new physics searches. In this
paper we review the status of theoretical predictions for cross sections and
kinematic distributions of processes in which an electroweak gauge boson is
produced in association with up to two $b$ jets in hadronic collisions, namely
$p\bar{p}, pp\rightarrow V+1b$ jet and $p\bar{p},pp\rightarrow V+2b$ jets with
$V=W^\pm, Z/\gamma^*, \gamma$. Available experimental measurements at both the
Fermilab Tevatron and the CERN Large Hadron Collider are also reviewed and
their comparison with theoretical predictions is discussed.
