  We construct general anisotropic cosmological scenarios governed by an
$f(R)=R^n$ gravitational sector. Focusing then on some specific geometries, and
modelling the matter content as a perfect fluid, we perform a phase-space
analysis. We analyze the possibility of accelerating expansion at late times,
and additionally, we determine conditions for the parameter $n$ for the
existence of phantom behavior, contracting solutions as well as of cyclic
cosmology. Furthermore, we analyze if the universe evolves towards the future
isotropization without relying on a cosmic no-hair theorem. Our results
indicate that anisotropic geometries in modified gravitational frameworks
present radically different cosmological behaviors compared to the simple
isotropic scenarios.
