  A comprehensive study of anisotropic quantum rings, QRs, subject to axial and
in-plane magnetic field, both aligned and transverse to the anisotropy
direction, is carried out. Elliptical QRs for a wide range of eccentricity
values and also perfectly circular QRs including one or more barriers
disturbing persistent QR current are considered. These models mimic anisotropic
geometry deformations and mass diffusion occuring in the QR fabrication
process. Symmetry considerations and simplified analytical models supply
physical insight into the obtained numerical results. Our study demonstrates
that, except for unusual extremely large eccentricities, QR geometry
deformations only appreciably influence a few low-lying states, while the
effect of barriers disturbing the QR persistent current is stronger and affects
all studied states to a similar extent. We also show that the response of the
electron states to in-plane magnetic fields provides accurate information on
the structural anisotropy.
