  We study vortex excitations in one-component Bose-Einstein condensates, with
a special emphasis on the role of anisotropic confinement for the existence,
stability and dynamical properties of vortices and particularly few-vortex
clusters. Symmetry breaking features are pervasive within this system even in
its isotropic installment, where cascades of symmetry breaking bifurcations
give rise to the multi-vortex clusters, but also within the anisotropic realm
which naturally breaks the rotational symmetry of the multi-vortex states. Our
first main tool for analyzing the system consists of a weakly nonlinear
(bifurcation) approach which starts from the linear states of the problem and
examines their continuation and bifurcation into novel symmetry-broken
configurations in the nonlinear case. This is first done in the isotropic limit
and the modifications introduced by the anisotropy are subsequently presented.
The second main tool concerns the highly nonlinear regime where the vortices
can be considered as individual topologically charged "particles" which precess
within the parabolic trap and interact with each other, similarly to fluid
vortices. The conclusions stemming from both the bifurcation and the
interacting particle picture are corroborated by numerical computations which
are also used to bridge the gap between these two opposite-end regimes.
