  We consider a Bose-Hubbard ladder subject to an artificial magnetic flux and
discuss its different ground states, their physical properties, and the quantum
phase transitions between them. A low-energy effective field theory is derived,
in the two distinct regimes of a small and large magnetic flux, using a
bosonization technique starting from the weak-coupling limit. Based on this
effective field theory, the ground-state phase diagram at a filling of one
particle per site is investigated for a small flux and for a flux equal to
$\pi$ per plaquette. For $\pi$-flux, this analysis reveals a tricritical point
which has been overlooked in previous studies. In addition, the Mott insulating
state at a small magnetic flux is found to display Meissner currents.
