Extremal black branes are of interest because they correspond to the
ground states of field theories at finite charge density in
gauge/gravity duality. The geometry of such a brane need not be
translationally invariant in the spatial directions along which it
extends. A less restrictive requirement is that of homogeneity, which
still allows points along the spatial directions to be related to each
other by symmetries. In this talk, I will describe a large new classes
of homogeneous but anisotropic extremal black brane horizons, which
could naturally arise in gauge/gravity dual pairs. In a system of
Einstein gravity with negative cosmological term coupled to one or two
massive Abelian gauge fields, we find solutions with an additional
scaling symmetry, which could correspond to the near-horizon
geometries of such extremal black branes. These solutions realize many
of the Bianchi classes. In one case, we construct the complete
extremal solution which asymptotes to AdS space.