  In this paper we study traversable wormholes in the context of $f(R)$
gravity. Exact solutions of traversable wormholes are found by imposing the
nonconstant Ricci scalar. These solutions asymptotically match spherical, flat
and hyperbolic FRW metric. By choosing some static $f(R)$ gravity models, we
verify the standard energy conditions for the asymptotically spherical, flat
and hyperbolic wormhole solutions. Unlike the Einstein gravity, we find that in
the context of $f(R)$ modified gravity, the asymptotically spherical, flat and
hyperbolic wormhole solutions can respect the null energy condition (NEC) at
the wormhole throat and near that. We find that in some static $f(R)$ models,
asymptotically flat and hyperbolic wormholes respect the weak energy condition
(WEC) through the whole space.
