  We consider interacting bosonic particles on a two-leg triangular ladder in
the presence of an artificial gauge field. We employ density matrix
renormalization group numerical simulations and analytical bosonization
calculations to study the rich phase diagram of this system. We show that the
interplay between the frustration induced by the triangular lattice geometry
and the interactions gives rise to multiple chiral quantum phases. Phase
transition between superfluid to Mott-insulating states occur, which can have
Meissner or vortex character. Furthermore, a state that explicitly breaks the
symmetry between the two legs of the ladder, the biased chiral superfluid, is
found for values of the flux close to $\pi$. In the regime of hardcore bosons,
we show that the extension of the bond order insulator beyond the case of the
fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the
consequences of our findings for experiments in cold atomic systems.
