  The effective theory for bilayer graphene (BLG), subject to parallel/in-plane
magnetic fields, is derived. With a sizable magnetic field the trigonal warping
becomes irrelevant, and one ends up with two Dirac points in the vicinity of
each valley in the low-energy limit, similar to the twisted BLG. Combining
twisting and parallel field thus gives rise to a Dirac system with tunable
Fermi velocity and cutoff. If the interactions are sufficiently strong, several
fully gapped states can be realized in these systems, in addition to the ones
in a pristine setup. Transformations of the order parameters under various
symmetry operations are analyzed. The quantum critical behavior of various
phase transitions driven by the twisting and the magnetic field is reported.
The effects of an additional perpendicular fields, and possible ways to realize
the new massive phases is highlighted.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons;High Energy Physics - Theory